A MAGYAR MITTEILUNGEN TUDOMÁNYOS AKADÉMIA DER CSILLAGVIZSGÁLÓ STERNWARTE INTÉZETÉNEK DER UNGARISCHEN AKADEMIE KÖZLEMÉNYEI DER WISSENSCHAFTEN BUDAPEST - SZABADSÁGHEGY NR. 69. S. KANYÓ U, B, V PHOTOMETRY OF THE MULTIPLE PERIODIC RR LYRAE STAR RV URSAE MAIORIS BUDAPEST, 1976. U,B,V PHOTOMETRY OF THE MULTIPLE PERIODIC RR LYRAE STAR RV URSAE MAIORIS SUMMARY Three-colour photoelectric photometry of the RRab variable star RV Ursae Maioris, is presented. Period and total light curve changes of the star during the Blazhko period and O-C diagrams of both the main and the secondary periods are investigated. It was found that a certain phase point / phi_s=0,94/ of the ascending branches of the light curves showed no oscillation during the Blazhko period, which is hardly compatible with the assumption of the superposition of beat periods. A long cycle of 6-8 years in the O-C variations of the ascending branch was also found. Similar long cycle variations are shown by other RR Lyrae stars exhibiting the Blazhko effect, this variation being reminiscent of the solar magnetic cycle. INTRODUCTION RV Ursae Maioris is an RRab Lyrae variable star whose light variation was among the firsts discovered. The variability of RV UMa was announced by Cerasky in 1907 /Cerasky 1907/, and its light elements were derived by Blazhko /1908/. According to the properties of the observed light curve and the period /P=0.4684d/ Blazhko classified the star as a short periodic delta Ceph variable. In 1920, Jordan and Subbotin pointed out independently the strong variation of the light curve of RV UMa /Jordan, 1920; Subbotin, 1927/ Photographic observations of RV UMa were initiated at the Konkoly Observatory by Julia Balázs and Detre with a 16 cm astrograph in 1936. A great number of observations were made in Budapest confirming the existence of a Blazhko effect, however, the secondary period could not be determined until photoelectric observations were made by Balázs and Detre in 1956-1957. Using all published observations they derived for the secondary period P_s=90.8d. They constructed O-C diagrams for both the fundamental and the secondary period over a time interval of 50 years. According to Preston the spectral type of RV UMa at minimum light is F4 from H-lines and A6 from the CaII-line giving Delta S=8 /Preston, 1959/. On 34 nights in 1959 and 1960 Preston obtained a total of 113 spectrograms of the star; with the X-spectrograph of the Mount Wilson 60-inch reflector concurrently Spinrad carried out photoelectric observations on the UBV system with the 20-inch reflector of the Leushner Observatory in Berkeley. In addition four light rises were observed by Preston with the 60-inch reflector in 1960. They used these series of photoelectric and spectroscopic observations to point out some peculiarities in the 90-day cycle /Preston and Spinrad, 1967/. THE PHOTOELECTRIC OBSERVATIONS The present author observed RV UMa photoelectrically during the period 1961-1969, at first in yellow and blue, later also in ultraviolet light. Additional measurements were obtained by Csank, Gefferth and Lovas on the B, V system in 1958-59. The observations ranged over all phases of the primary and secondary periods. In this way it was possible to study the variations of complete light- and colour-curves in the 90-day cycle. The distribution of the observations is listed in Table I. Table I Number of observations Year Number of nights Yellow Blue Ultra- Total violet 1958 6 69 69 - 138 1959 10 138 138 - 276 1976 50 1356 1356 - 2712 1962 47 593 593 562 1748 1963 17 26 275 275 576 1964 15 110 110 110 330 1965 1 16 16 - 32 1968 2 33 33 14 80 1969 2 37 37 - 74 Total 150 2378 2627 961 5966 All observations were made with the 24-inch reflector of the Konkoly Observatory. The unrefrigerated photometer employed was equipped with an RCA 1P21 photomultiplier up to 1961, after that time with an EMI 9502B phototube. The following filters were used Colour Type lambda eff yellow Schott GG 11 5600 A blue " BG 12+GG 13 4300 A ultraviolet " UG 1 3950 A The photomultiplier output was amplified by a d.c. amplifier. The linearity of the instrument seemed to be warranted within the mesauring interval. The comparison star for our observations was the visual double star BD +55 1616. Spinrad used the same comparison star while BD +54 1610, used by Preston as a comparison star, was chosen as the check star. Both stars are within 20' to the variable. The photoelectric data for these stars were adopted from the measurements of Preston and Spinrad /Table II/. Table II V B-V U-B BD +55 1616 9.963 + 0.507 - 0.114 BD +54 1610 9.62 + 0.580 + 0.095 Observations of standard stars published by Johnson and Morgan /1953/ were used to transfer the differential magnitudes and colours from the instrumental system u,b,v to the international U, B, V system by the formulae: Delta V = Delta v + epsilon Delta/B-V/ /1/ Delta/B-V/ = mu Delta/b-v/ /2/ Delta/U-B/ = psi Delta/u-b/ /3/ The values of the coefficients were determined from time to time, though not frequently enough to be able to trace small variations caused by variability of sky transparency. Therefore, only the most significant variations of the coefficients were taken into account - specially that due to a transition from a silvered mirror to an aluminized one in 1961. Beginning with 1963 we have obtained sufficient data for the coefficients. The different sets of these coefficients are given in Table III, while the reduced observations are listed in Table IV. Table III Time interval epsilon mu psi From Feb. 1958 to May 1963 - 0,132 1,05 1,08 1964 - 0,14 1,12 1,16 Apr. 1965 - 0,136 1,17 1,09 January 1968 - 0,166 1,208 1,10 March 1968 - 0,156 1,152 1,00 January 1969 - 0,130 1,194 1,02 May 1969 - 0,177 1,181 0,955 LIGHT-CURVE VARIATIONS The main purpose of this investigation was to study the variations of the light curve in V and the B-V and U-B colour curves in the 90 -day cycle for all phases / phi / of the 0.468d period. However the observations were concentrated on the phases phi = 0,85 - 0,05, i. e. on the minimum ascending branch and maximum of the light curve. Some individual V, B-V and U-B curves for these phases are represented in Fig. 1. To obtain complete light curves for all phases /the phase of highest maximum being taken as psi=0/ of the 90d secondary period the same procedure was applied as by Julia Balázs and Detre /1939/ for AR Herculis. From the observed light curves the magnitudes were read off for a set of phi - phases and these magnitudes were then plotted versus psi. In this way we obtained a sequence of curves representing the variation in the light curve for definite phi-phases as a function of psi. For derivation of proper phi and psi-values the O-C diagrams must first be constructed for both the fundamental and secondary periods. For C, the elements of Balázs and Detre /1957/ were used, viz. /J.D. /maximum light/ = 2417861,4292+0,468063203d E /I/ and Figure 1 The observed light curves in UBV according to different phase points of Blazhko period. J. D. /brightest maximum/ = 2418060 + 90,12 x N. /II/ where E and N are epoch counts in the respective periods. For each year the actual fundamental and secondary periods were determined by using the O-C /I/ and O-C /II/ curves. For instance the fundamental period obtained for 1961 /when the greatest number of observations were collected/ was P = 2437327,692 + 0,468061103d E and the secondary period P_s = 2437359 + 92,12d . N. The brightest maxima were chosen from every observational season and are given in Table V. The O-C diagrams constructed for these maxima are shown in Fig 2. They are typical for RR Lyrae stars having a secondary period and their structure can be considered as resulting from the cumulative effects of random period changes. Even so, the comparison of O-C/II/ reveals two important characteristics: 1. The long cycles resulting from cumulative effects of random period changes are opposite in phase in the two diagrams. That is a change in the secondary period is accompanied by an opposite change in the fundamental period. 2. The changes expressed in units of the respective period are much larger for the secondary period than for the main one. These characteristics are especially conspicuous for RW Draconis and in some respect also for RR Lyrae /see Detre, 1970/. They are considered to be of fundamental importance for the interpretation of the secondary period. A few V = V /psi/_(phi =const) - diagrams are represented in Fig. 3a. The scatter in V is largely due to the random variations in the periods which makes an exact determination of phi and psi impossible. This is proved by the fact that the scatter is largest in the ascending branch, between phases phi = 0,85 to 0,975, which part of the light curve is especially sensitive to random phase variations. Table V. Observed maxima J.D. Year 2430000+ Delta Mv Delta Mb Delta Muv 1958 6229,6 +0,420 +0,120 6245,5 +0,290 -0,005 6282,5 +0,015 -0,390 1959 6655,6 +0,085 -0,300 6680,4 +0,385 +0,105 6684,6 +0,428 +0,100 6692,5 +0,372 +0,080 6724,4 -0,050 -0,460 1961 7327,7 +0,335 -0,015 7331,4 +0,295 -0,055 7339,- - - 7344,5 +0,060 -0,415 7345,5 +0,020 -0,435 7360,5 -0,060 -0,640 7365,6 -0,045 -0,525 7376,4 +0,010 -0,430 7395,6 +0,226 -0,175 7396,5 +0,255 -0,140 7397,4 +0,260 -0,130 7404,5 +0,365 -0,025 7411,5 +0,410 +0,045 7418,5 +0,345 0,00 7424,5 +0,260: -0,150 7456.- - - 7463,4 0,000 -0,470 1962 7652,5 -0,010 -0,375 -0,380 7680,6 -0,395 +0,035 +0,175 7702,6 +0,185 -0,250 -0,125 7732,6 -0,065 -0,510 -0,420 7756,4 +0,170 -0,190 -0,110 7769,5 +0,360 +0,050 - 7780,3 +0,365: -0,025 +0,040 7806,5 -0,010 -0,385 -0,280: 7808,4 -0,050 -0,445 -0,410 7815,4 -0,090 -0,500 -0,470 7829,5 -0,170 -0,560 -0,520: 1963 8003,6 -0,070 -0,500 -0,475 8019,5 +0,125 -0,265 -0,175 8047,6 - +0,130 +0,220 8085,5 - -0,450 -0,350 8086,4 - -0,445 -0,380 8090,6 - -0,400 -0,370 8114,5 - -0,138 -0,050 1964 8415,5 +0,325 -0,040 +0,100 8457,6 -0,090 -0,500 -0,360 8496,4 +0,350 0,000 +0,135 8503,5 +0,300 -0,055 +0,115 8548,4 -0,030 -0,520 -0,340 Figure 2 The O-C values for the fundamental O-C/I/ and for the secondary periods O-C/II/ Figure 3a Figure 3 Similar marks on the diagram represent a certain phi phase value of the fundamental period obtained from the light curves of different Blazhko phase psi. Figures 3a,b,c are in Delta V, Delta B and Delta U respectively. Figure 4 The diagram shows the flattened light curves of different secondary period phase psi constructed from figures 3a,b,c. The same procedure was carried out in B and U, as well /Fig.3b, 3c/ Using these curves the V /phi/_(psi=const') B-V /phi/_(psi=const) and U-B /phi/_(psi=const) diagrams /Figs. 4a and b/ were constructed on which all the following discussions are based. The two-colour diagrams at different phases of the secondary period are shown in Fig. 5. On the loops the phases of the main period are also indicated. The dashed line is the relation for the main sequence stars. The V magnitudes and B-V colour indices at minimum light and maximum light and the U-B ranges delta_2/ defined by Preston, Ann. Rev.of Astr. and Astroph. Vol. 2, 1964/ are plotted versus psi in Fig. 6. The V and B-V ranges are correlated and the values of V are more strongly variable at maximum light than at minimum light as in the case of other RR Lyrae stars with Blazhko effect. Our photometric results are in good agreement with those obtained by Preston and Spinrad /Ap. J. 147, 1025, 1967/. Nevertheless there are some slight differences especially in the delta_2 values because accurate observations in U-B could not be made under the unsatisfactory observing conditions near Budapest. Figures 7a and b show the amplitude variation Delta A of the m/psi/ curves and the phase psi of the maxima of the same curves plotted against phi. Delta A have two maxima in each colour. The first of the maxima is at phase phi = 0,90 on the ascending branch and the second one - which is higher, is at the phase of the light maximum / phi=0,00/. It is evident from the figure that the light curves do not change significantly between the phi = 0,35 - 0,55 phase interval during the Blazhko cycle, It is however, rather surprising that there is a very deep minimum at phase 0,94 on the ascending branch between the two maxima mentioned above. This deep minimum indicates that there exists a point on the ascending branch which does not show any significant oscillation during the Blazhko cycle while the ascending branch before and after it and especially the light maximum shows considerable oscillation. It is very interesting to compare our results with those obtained for AR Herculis by Almár /1961/. The same curves obtained for AR Her, also show double maxima but at other phases. The essential difference is that the first maximum of AR Her, is higher than the second one and the deep minimum is situated at the phase of light maximum. Figure 5 The two-colour diagrams at different phases of the secondary period. The dashed line represents the main sequence. Table VI./1 \phi 0,00 0,025 0,05 0,10 0,15 0,20 0,25 0,60 0,65 0,70 0,75 0,80 0,85 0,875 0,90 0,925 0,942 0,950 0,975 psi\ 0,00 -0,050 -0,070 -0,050 -0,045 -0,025 0,020 0,040 -0,050 -0,040 -0,090 -0,080 -0,070 -0,100 -0,085 -0,075 -0,030 -0,010 -0,010 -0,50 0,00 0,05 -0,050 -0,065 -0,050 -0,035 -0,025 0,000 0,030 0,050 -0,025 -0,090 -0,080 -0,070 -0,090 -0,075 -0,075 -0,025 -0,010 -0,010 -0,050 0,05 0,10 -0,045 -0,060 -0,050 -0,030 -0,020 0,000 0,015 -0,040 -0,010 -0,085 -0,080 -0,070 -0,065 -0,070 -0,025 -0,010 -0,010 -0,050 0,10 0,25 -0,020 -0,030 -0,035 -0,010 0,010 0,020 0,000 0,000 0,025 -0,070 -0,075 -0,065 -0,020 -0,025 -0,030 -0,010 -0,010 -0,010 -0,030 0,25 0,40 0,000 0,000 0,000 0,000 0,040 0,040 0,010 0,010 0,020 -0,040 -0,060 -0,060 -0,010 -0,025 0,010 -0,010 -0,010 -0,015 0,40 0,50 0,020 0,030 0,020 0,005 0,050 0,060 0,060 0,000 0,010 -0,020 -0,050 -0,040 -0,020 -0,025 0,025 -0,010 -0,010 -0,005 0,50 0,60 0,020 0,065 0,040 0,025 0,050 0,080 0,080 0,000 0,000 -0,030 -0,060 -0,050 -0,020 -0,035 0,010 0,025 -0,010 -0,010 -0,010 0,60 0,70 0,000 0,050 0,035 0,030 0,040 0,080 0,080 -0,010 -0,015 -0,060 -0,065 -0,055 -0,050 -0,050 -0,020 0,000 -0,010 -0,010 -0,020 0,70 0,75 -0,015 0,020 0,020 0,015 0,030 0,075 0,075 -0,020 0,025 -0,060 -0,070 -0,60 -0,070 -0,060 -0,040 -0,010 -0,010 -0,010 -0,030 0,75 0,80 -0,025 -0,010 0,000 -0,005 0,015 0,070 0,070 -0,030 -0,035 -0,070 -0,075 -0,065 -0,090 -0,070 -0,070 -0,010 -0,010 -0,035 0,80 0,90 -0,040 -0,050 -0,030 -0,045 -0,010 0,040 0,060 -0,050 -0,050 -0,085 -0,080 -0,070 -0,110 -0,085 -0,075 -0,025 -0,010 -0,010 -0,045 0,90 0,95 -0,050 -0,065 -0,040 -0,045 -0,020 0,030 0,050 -0,060 -0,050 -0,090 -0,085 -0,075 -0,110 -0,090 -0,075 -0,025 -0,010 -0,010 -0,050 0,95 Table VI./2 \phi 0,00 0,025 0,05 0,10 0,15 0,20 0,25 0,30 0,40 0,50 0,60 0,65 0,70 0,75 0,80 0,85 0,875 0,90 0,925 0,942 0,950 0,975 psi\ 0,00 0,100 0,100 0,090 0,150 0,185 0,220 0,240 0,280 0,339 0,387 0,395 0,420 0,430 0,435 0,410 0,430 0,440 0,420 0,335 0,235 0,235 0,125 0,00 0,05 0,90 0,095 0,085 0,150 0,185 0,220 0,240 0,275 0,345 0,384 0,400 0,420 0,435 0,440 0,415 0,430 0,435 0,420 0,340 0,235 0,235 0,125 0,05 0,10 0,090 0,095 0,080 0,150 0,180 0,220 0,240 0,260 0,345 0,382 0,400 0,420 0,435 0,400 0,415 0,430 0,430 0,415 0,340 0,235 0,235 0,125 0,10 0,25 0,120 0,115 0,125 0,165 0,205 0,250 0,270 0,270 0,353 0,360 0,410 0,410 0,425 0,425 0,400 0,415 0,395 0,380 0,305 0,235 0,235 0,150 0,25 0,40 0,160 0,160 0,180 0,200 0,260 0,315 0,300 0,285 0,366 0,344 0,390 0,400 0,390 0,400 0,360 0,375 0,350 0,330 0,250 0,235 0,235 0,205 0,40 0,50 0,170 0,175 0,185 0,225 0,260 0,300 0,300 0,310 0,338 0,350 0,375 0,370 0,360 0,380 0,340 0,340 0,315 0,275 0,230 0,235 0,235 0,240 0,50 0,60 0,160 0,165 0,170 0,220 0,250 0,280 0,280 0,325 0,313 0,355 0,350 0,380 0,370 0,385 0,345 0,345 0,330 0,290 0,245 0,235 0,235 0,215 0,60 0,70 0,150 0,140 0,150 0,200 0,235 0,265 0,270 0,325 0,324 0,348 0,355 0,390 0,390 0,405 0,370 0,375 0,370 0,350 0,275 0,235 0,235 0,180 0,70 0,75 0,145 0,130 0,135 0,190 0,225 0,255 0,260 0,320 0,326 0,337 0,360 0,390 0,400 0,410 0,380 0,395 0,395 0,370 0,285 0,235 0,235 0,160 0,75 0,80 0,135 0,120 0,125 0,180 0,215 0,250 0,260 0,310 0,314 0,340 0,370 0,400 0,415 0,415 0,390 0,410 0,410 0,390 0,300 0,235 0,235 0,150 0,80 0,90 0,120 0,110 0,110 0,160 0,200 0,230 0,250 0,300 0,322 0,360 0,380 0,415 0,435 0,425 0,400 0,425 0,435 0,410 0,325 0,235 0,235 0,130 0,90 0,95 0,110 0,100 0,100 0,155 0,195 0,225 0,250 0,290 0,340 0,367 0,390 0,420 0,430 0,430 0,410 0,430 0,445 0,415 0,335 0,235 0,235 0,125 0,95 Figure 6 The curves show typical variation of V_max, V_min, /B-V/_max, /B-V/_min and delta_2 Preston index, during the secondary period. Figure 7a Figure 7a shows the amplitudes of light curves belonging to different phases phi of figures 3a and 3b. Figure 7b Psi_max points show the psi secondary phase of maxima of phi phase curves in the figure 3. Figure 8 The O-C secular variations of three magnitude levels of the ascending branch of the main period. This may be connected with the behaviour of the double light maximum of AR Her which appears at certain phases of the secondary period while no double maximum can be observed for RV UMa. The most important theoretical consequence of the fact that there is no oscillation on a certain phase point of the ascending branch of RV UMa during the Blashko period suggests that the fundamental and the secondary period can not arise due to two beat periods. That is to say in the case of superposition of beat periods the ascending branch of the main period would need to oscillate to produce the required effect in each of its phase points during the Blazhko period. Figure 8 shows the /O-C/ secular variation of three magnitude levels of the ascending branch of the main period. The /O-C/ variations of the magnitude levels m:0,8, 0,5, 0,3 are cyclic and coincident with each other. The length of the cycle is approximately 6-8 years. The cyclic variation of these fixed magnitude points of the ascending branch is due to the secular cyclic variation of the light curve form. When the /O-C/ is more positive, the rising branch of the light curve is always steeper during the secondary period and vice versa; the less positive the /O-C/ variation the more sinusoidal in form the light curve. Whatever the cause of the cyclic variation of the light curve form, the length of this cyclic variation of RV UMa is commensurable with that of RR Lyrae. However, this length of cyclic variation corresponds to the magnitude of the magnetic solar cycle therefore the suspicion that the cyclic variation is a magnetic variation of the variable star, as suggested by Detre, seems reasonable. TABLE VII. Year E t^max t^max-C t^+2-C t^+5-C 243 ... 1958 39243 6229,6210 -0,0125 -0,0255 - 39277 6245,5425 -0,0510 -0,0261 -0,0411 39356 6282,5095 -0,0151 -0,0316 -0,0391 1959 40153 6655,5540 -0,0170 -0,0360 -0,0435 40206 6680,3650 -0,0133 -0,0318 -0,0483 40215 6684,5810 -0,0099 -0,0229 -0,0454 40232 6692,5450 -0,0030 -0,0215 -0,0425 40300 6724,3630 -0,0133 -0,0373 - 1961 41589 7327,6970 -0,0127 -0,0317 -0,0497 41597 7331,4425 -0,0118 - - 41614 7339,- - -0,0343 -0,0443 41625 7344,5470 -0,0130 -0,0355 -0,0420 41627 7345,4860 -0,0102 -0,0352 -0,0442 41644 7353,4430 - -0,0357 -0,0407 41655 7358,5940 -0,0079 -0,0359 -0,0459 41659 7360,4650 -0,0092 -0,0390 -0,0427 41670 7365,6125 -0,0104 -0,0363 -0,0414 41674 7367,4825 -0,0126 - - 41676 7368,4180 -0,0132 - - 41689 7374,5040 -0,0121 - - 41693 7376,3725 -0,0113 -0,0373 -0,0423 41734 7395,5600 -0,0189 -0,0394 -0,0479 41736 7396,4970 -0,0180 -0,0375 -0,0500 41738 7397,4350 -0,0162 - - 41749 7402,5880 -0,0119 -0,0324 -0,0485 41753 7404,4570 -0,0151 - - 41768 7411,4775 -0,0156 -0,0309 -0,0526 41783 7418,5020 -0,0120 -0,0300 -0,0515 41796 7424,5870 -0,0118 -0,0333 -0,0463 41864 7456,- - -0,0363 -0,0411 41869 7463,4365 -0,0116 -0,0366 -0,0411 t^+8-C t t-C N psi Delta B^max Delta B^min C - 0,594 -0,0395 201 0,616 +0,120 - ,6335 - 0,513 -0,0346 201 0,792 -0,005 - ,5476 - 0,4895 -0,0351 202 0,203 -0,390 - ,5246 -0,0525 0,5313 -0,0397 206 0,342 -0,300 +0,850 ,5710 -0,0833 0,340 -0,0383 206 0,618 +0,105 - ,3783 -0,0684 0,5535 -0,0374 206 0,664 +0,100 +0,880 ,5909 -0,0730 0,5135 -0,0345 206 0,752 +0,080 +0,910 ,5480 - - - 207 0,106 -0,460 - ,3763 -0,0817 0,6675 -0,0422 213 0,800 -0,015 +0,975 ,7097 - - - 213 0,842 -0,055 - ,4543 - 0,3700 -0,0413 213 0,932 - - ,4113 -0,0540 0,5205 -0,0395 213 0,988 -0,415 +1,065 ,5600 -0,0542 0,4574 -0,0388 213 0,999 -0,435 +1,075 ,4962 - 0,415 -0,0382 214 0,089 - - ,4532 -0,0559 0,5595 -0,0424 214 0,143 -0,490 +1,050 ,6019 -0,0507 0,4300 -0,0442 214 0,164 -0,640 +1,075 ,4742 -0,0489 0,5845 -0,0384 214 0,221 -0,525 +1,210 ,6229 - - - 214 0,242 - - ,4951 - - - 214 0,252 - - ,4312 - - - 214 0,320 - - ,5161 -0,0533 0,348 -0,0403 214 0,341 -0,430 +0,990 ,3883 - 0,5345 -0,0444 214 0,553 -0,175 - ,5789 -0,0700 0,470 -0,0450 214 0,564 -0,140 +0,950 ,5150 - - - 214 0,574 -0,130 +1,025 ,4512 -0,0709 -0,5585 -0,0414 214 0,631 -0,090 +0,925 ,5999 - - - 214 0,652 -0,025 - ,4721 -0,0801 0,4505 -0,0426 214 0,730 +0,045 +0,900 ,4931 -0,0765 0,4705 -0,0435 214 0,808 0,000 +0,950 ,5140 -0,0678 0,5578 -0,0410 214 0,876 -0,150 +1,000 ,5988 -0,0483 0,3872 -0,0399 215 0,230 - +1,180 ,4271 -0,0485 0,4090 -0,0391 215 0,307 -0,470 - ,4481 TABLE VII.(cont.) Year E t^max t^max-C t^+2-C T^+5-C t^+8-C 243 1962 42283 7652,5275 -0,0181 - - - 42343 7680,6100 -0,0194 -0,0294 -0,0509 -0,0819 42390 7702,6165 -0,0134 -0,0334 -0,0422 -0,0584 42454 7732,5720 -0,0124 -0,0354 -0,0429 -0,0494 42505 7756,4390 -0,0166 -0,0371 -0,0501 -0,0641 42533 7769,5440 -0,0189 -0,0309 -0,0484 -0,0664 42556 7780,3100 -0,0169 -0,0299 - - 42612 7806,5270 -0,0114 -0,0334 -0,0406 -0,0494 42616 7808,3970 -0,0137 -0,0357 -0,0437 -0,0527 42627 7813,5415 -0,0194 -0,0324 -0,0364 -0,0434 42631 7815,4210 -0,0106 -0,0346 -0,0391 -0,0471 42661 7829,4600 -0,0135 -0,0370 -0,0430 -0,0490 1963 43031 8003,6475 -0,0094 -0,0354 -0,0405 -0,0519 43067 8019,500 -0,0152 - - - 43127 8047,5805 -0,0185 -0,0230 -0,0470 - 43208 8085,4910 -0,0131 -0,0331 -0,0386 -0,0481 43210 8086,4295 -0,0107 -0,0337 -0,0373 -0,0457 43219 8090,6390 -0,0138 -0,0346 -0,0398 -0,0453 43270 8114,5050 -0,0190 -0,0355 -0,0442 -0,0558 1964 43913 8415,4750 -0,0171 -0,0320 -0,0501 - 44003 8457,5975 -0,0168 -0,0388 -0,0427 -0,0518 44086 8496,4400 -0,0211 -0,0376 -0,0598 -0,0836 44101 8503,4750 -0,0160 -0,0345 -0,0540 - 44197 8548,4035 -0,0151 -0,0331 - - t t-C N psi Delta B^max Delta B^min C - - 217 0,405 -0,375 - ,5456 0,5880 -0,0414 217 0,716 +0,035 +1,010 ,6294 0,5895 -0,0389 217 0,961 -0,250 - ,6284 0,5445 -0,0399 218 9,293 -0,510 +1,145 ,5844 0,4105 -0,0451 218 0,559 -0,190 +0,920 ,4556 0,5205 -0,0409 218 0,704 +0,050 - ,5614 - - 218 0,822 -0,025 - ,3269 0,5008 -0,0376 219 0,113 -0,385 +1,050 ,5384 0,3720 -0,0387 219 0,134 -0,445 +1,150 ,4107 0,5240 -0,0354 219 0,192 -0,385 +1,200 ,5594 0,3940 -0,0376 219 0,212 -0,500 - ,4316 0,4330 -0,0405 219 0,368 -0,560 +0,975 ,4745 0,6190 -0,0379 221 0,301 -0,500 - ,6569 - - 221 0,477 -0,265 - ,5079 0,5505 -0,0405 221 0,489 +0,130 - ,5910 0,4675 -0,0366 222 0,209 -0,450 +1,260 ,5041 0,4066 -0,0336 222 0,220 -0,445 +1,150 ,4402 0,6150 -0,0378 222 0,265 -0,400 +1,160 ,6528 0,4826 -0,0414 222 0,420 -0,138 - ,5240 0,4458 -0,0428 225 0,871 -0,040 +0,900 ,4886 0,5740 -0,0430 226 0,338 -0,500 +1,150 ,6143 0,4125 -0,0511 226 0,769 0,000 - ,4636 0,4377 -0,0468 226 0,847 -0,055 - ,4845 - - 227 0,346 -0,520 - ,4186 TABLE VIII. A^m-phi , CI_phi and psi^max-phi of RV UMa 1958 - 64 years phi Delta A^v Delta A^b Delta A^uv Delta /B-V/ Delta /U-B/ psi^max 0,000 +0,490 +0,590 +0,635 +0,135 +0,260 0,00 0,025 +0,470 +0,580 +0,585 +0,110 +0,350 0,02 0,050 +0,425 +0,515 +0,530 +0,125 +0,290 0,02 0,100 +0,300 +0,425 +0,420 +0,140 +0,145 0,00 0,150 +0,300 +0,310 +0,350 +0,140 +0,130 0,05 0,200 +0,220 +0,260 +0,210 +0,130 +0,100 0,16 0,250 +0,195 +0,140 +0,200 +0,125 +0,165 0,24 0,300 +0,125 +0,160 +0,200 +0,090 +0,255 0,25 0,350 +0,125 +0,140 - +0,070 +0,220 0,34 0,400 +0,105 +0,110 - +0,060 +0,220 0,35 0,450 +0,115 +0,110 - - - 0,38 0,500 +0,075 +0,110 - +0,050 +0,135 0,46 0,550 +0,080 +0,170 - - - 0,58 0,600 +0,135 +0,195 - +0,095 +0,210 0,58 0,650 +0,195 +0,225 - - - 0,58 0,700 +0,160 +0,220 - +0,150 +0,140 0,58 0,750 +0,165 +0,160 +0,200 +0,105 +0,220 0,60 0,800 +0,235 +0,260 +0,218 +0,125 +0,170 0,62 0,850 +0,310 +0,350 +0,300 +0,160 +0,135 0,64 0,875 +0,325 +0,465 +0,350 +0,110 +0,235 0,66 0,900 +0,285 +0,500 +0,440 +0,240 +0,160 0,68 0,925 +0,255 +0,310 +0,225 +0,190 +0,070 0,69 0,940 +0,175 +0,220 +0,160 +0,310 +0,190 0,75 0,950 +0,185 +0,210 +0,190 +0,070 +0,090 0,00 0,960 +0,320 +0,400 +0,360 +0,220 +0,215 0,06 0,975 +0,460 +0,480 +0,545 +0,110 +0,220 0,06 REFERENCES /1/ AN 176. 109, 1907 /2/ AN 177. 107, 1908 /3/ Allegheny Publ. VII. p.40. /4/ AN 231. 153. 1927. /5/ Budapest Mitt. Nr. 34. /6/ Ap.J. 130, 507, 1959. /7/ Per.zvj. 9. No.4. 1953. /8/ Ap.J. 117. 313. /9/ Astron.techn. 1962. p. 203. /10/ Budapest Mitt. Nr. 8 /1939/ /11/ Budapest Mitt. Nr. 51. /1961./ /12/ Ap.J. 147. 1025. 1967.