COMMISSION 27 OF THE I. A. U. INFORMATION BULLETIN ON VARIABLE STARS Number 1649 Konkoly Observatory Budapest 1979 July 30 FURTHER EXAMINATION OF THE EQUATIONS FOR THE TIMES OF MAXIMUM LIGHT FOR SX PHOENICIS From data published elsewhere (Coates et al., 1979), we have constructed the equations for the times of maximum light: t_MAX(pre-1960)= 2433923.9618+0.054964519*E1 - 0.00337 sin2pi(0.28503379*E_1+0.074) (1) and t_MAX(post-1960)=2438636.6170+0.054964438*E_2 - 0.00325 sin2pi(0.28503575*E_2-0.107) (2) which yield values for the times of maximum light of SX Phe, t_MAX (calculated), that differ from the observations with an rms deviation of 0.0006 days in the case of equation (1) and 0.0009 days in the case of equation (2). E_1 is the number of cycles of the pre-1960 fundamental period since the epoch HJD 2433923.9618; E_2 is the number of cycles of the post-1960 fundamental period since the epoch HJD 2438636.6170, and the number of cycles between these two epochs is 85740. We have made preliminary examinations of the residuals [t_MAX (observed) -t_MAX (calculated)] for all 314 observations of maximum light (Appendix 1) for systematic deviations which might provide evidence for another mode of oscillation of SX Phe. We find that for all groups of observations but two the residuals appear to be normally distributed about zero. A standard Student's t-test yields probabilities that each group of residuals is a sample from a normal distribution of residuals of mean zero, (Table 1 ). It is seen that the two groups of observations made by Stock and Tapia between 1966 September 18 and 1966 November 1 appear to be exceptional. Table 1 ANALYSIS OF RESIDUALS Observer No. of Sample Sample Probability Maxima Mean RMS Dev. (from t-test) (Units of 10-4 day) Eggen 8 1.1 10.8 0.808 Walraven 71 -0.1 5.3 0.624 Wilson and Walker 6 4.8 7.4 0.185 Wood 5 -2.6 4.4 0.237 Stock and Tapia 7 4.0 7.3 0.192 Stock and Tapia *41 -5.0 6.9 0.000043 Stock and Tapia *29 9.2 5.9 4.4 x 10^-9 Stock and Tapia 21 -3.4 7.6 0.053 Stock and Tapia 23 -2.9 7.8 0.095 Stock et al. 5 12.6 7.5 0.020 Elst 46 -1.0 8.4 0.458 Haefner 5 -0.4 14.2 0.958 Dale 7 2.3 8.3 0.488 Halprin 33 0.2 9.1 0.903 Halprin 7 0.3 10.7 0.937 *Refer to Table 2 Table 2 COMPARISON OF RESIDUALS FOR STOCK AND TAPIA No. of Sample Mean Sample RMS Dev. Probability Maxima (Units of 10^-4 Day) (Units of 10^-4 Day) Old Adjusted Old Adjusted Old Adjusted 41 -5.0 1.7 6.9 6.5 4.3x10^-5 0.086 29 9.2 -0.9 5.9 6.5 4.4x10^-9 0.489 The residuals for these observations are plotted in Figure 1. These results may be explicable in terms of some previously unnoticed instability in the behaviour of SX Phe, perhaps the temporary excitation of a third mode of oscillation. However, we cannot exclude the possibility that these groups of data are based on an incorrect conversion between Geocentric and Heliocentric time. If we assume that all the observations have been converted to Heliocentric time using a constant factor appropriate to JD 2439410, which is the approximate mid-time for these groups, then the form of Figure 1 may be explained. Assuming that the conversion to HJD was made in this way, we have recovered adjusted residuals for these observations, and these are shown in Figure 2. Table 2 then gives the new probability values from a t-test, and it is clear that the adjusted residuals are much more likely to be a sample from a normal distribution of residuals of mean zero. [FIGURE 1] Figure 1: Plot of residuals for Stock and Tapia maxima Sept.-Nov. 1966. The curve represents the required correction to the data assuming that a constant geocentric to heliocentric time conversion factor calculated for mid-time was originally used. [FIGURE 2] Figure 2: Plot of the adjusted residuals for Stock and Tapia using the corrections acquired from the curve in Fig. 1. Analysis of the residuals for periodicity has not as yet provided sufficient evidence to support the existence of an additional mode of oscillation of SX Phe. D.W. COATES, L. HALPRIN, K. THOMPSON Department of Physics, Monash University, Clayton, Victoria, Australia, 3168 Reference: Coates, D.W., Dale, M., Halprin, L., Robinson, J. and. Thompson, K., 1979, Mon.Not.R. astr. Soc. 187, 83 [BIBCODE 1979MNRAS.187...83C ] Appendix. We give for reference the residuals determined from our equations for all observed times of maximum light. Pre-1960 Residuals Observed Time Residual Observed Time Residual (HJD-2430000) (Days) (HJD-2430000) (Days) 3923.95960 -0.00070 4238.52040 -0.00030 3924.01310 -0.00100 4238.58170 0.00090 3926.92770 -0.00140 4238.63560 -0.00010 3926.98920 0.00110 4240.39220 -0.00010 3927.03920 0.00010 4240.50440 0.00040 3927.09340 0.00170 4251.43670 -0.00060 3927.15240 0.00070 4254.29570 -0.00040 3927.20720 0.00040 4254.35180 0.00000 4224.51090 0.00070 4254.41140 -0.00010 4224.56390 -0.00030 4254.46280 -0.00090 4227.42540 0.00120 4254.51530 0.00020 4227.52810 0.00030 4254.57440 0.00010 4227.58830 0.00060 4278.26200 0.00090 4227.64320 0.00030 4278.32170 0.00060 4228.41280 0.00030 4278.37280 -0.00070 4228.51830 -0.00070 4278.42550 0.00090 4228.57820 -0.00020 4278.48300 -0.00070 4228.63010 0.00030 4283.26180 -0.00020 4229.34860 0.00070 4283.32200 -0.00010 4229.39940 -0.00010 4283.42670 0.00010 4229.51130 0.00030 4283.48310 -0.00120 4229.56700 0.00000 4293.32280 -0.00050 4231.37560 0.00060 4293.38100 -0.00050 4231.43450 0.00020 4293.43210 0.00030 4231.49110 0.00010 4293.48460 -0.00100 4231.54080 -0.00010 4294.31490 -0.00020 4231.59600 -0.00040 4294.36960 0.00040 4232.36500 -0.00070 4294.41960 0.00020 4232.42550 -0.00010 4294.47730 -0.00010 4232.47790 -0.00030 4295.30450 -0.00080 4232.58790 -0.00040 4295.35560 -0.00050 4232.64480 -0.00070 4295.40920 0.00010 4235.33940 0.00040 4295.46880 -0.00030 4235.38910 0.00010 4295.52380 0.00000 4235.44330 0.00010 4966.85690 0.00150 4235.50320 0.00000 4966.91600 0.00070 4235.55680 -0.00020 4966.97050 -0.00030 4235.60790 0.00050 4967.84680 0.00020 4236.43430 -0.00060 4967.90590 -0.00030 4236.49280 -0.00050 4967.95880 0.00110 4236.54420 0.00040 6158.98190 -0.00020 4236.59700 -0.00020 6175.96790 0.00030 4236.65880 0.00150 6176.02570 -0.00050 4238.41770 0.00060 6183.99100 0.00000 4238.46770 -0.00030 6184.04470 -0.00080 8636.66920 0.00020 9422.77700 0.00050 8636.72700 0.00080 9423.65170 0.00190 8636.78500 0.00000 9425.57390 0.00050 8636.83760 0.00140 9425.63380 0.00080 8639.64200 0.00070 9425.68890 0.00010 8639.69660 -0.00090 9425.73970 0.00090 8639.74800 0.00060 9426.56400 -0.00050 9387.65420 0.00100 9426.62570 0.00180 9388.58350 -0.00130 9426.72840 0.00080 9388.64200 -0.00160 9428.54930 0.00170 9388.80700 -0.00030 9428.60080 0.00080 9389.57660 0.00000 9428.65180 0.00050 9389.63110 -0.00080 9428.71200 0.00170 9389.68100 -0.00090 9429.53760 0.00080 9389.73720 -0.00160 9429.56750 0.00050 9389.79770 -0.00010 9429.64300 0.00110 9389.84790 -0.00130 9429.70300 0.00140 9391.60470 -0.00130 9431.56550 0.00030 9391.66000 -0.00200 9431.62670 0.00150 9391.72090 -0.00060 9431.67910 0.00040 9391.77200 -0.00140 9431.73070 0.00130 9391.82430 -0.00090 9756.67880 -0.00090 9392.59520 0.00060 9756.74090 0.00130 9392.65370 -0.00020 9756.79220 -0.00150 9392.70790 -0.00070 9756.84350 -0.00060 9392.75980 -0.00060 9758.76780 -0.00020 9392.81570 -0.00040 9758.82320 -0.00210 9393.64450 -0.00070 9759.75710 -0.00030 9393.69680 -0.00070 9759.81690 -0.00010 9393.74870 -0.00020 9761.79620 -0.00030 9393.80830 0.00040 9762.78310 -0.00030 9394.57630 -0.00100 9762.83520 0.00010 9395.56750 -0.00120 9763.72030 -0.00010 9395.62160 -0.00020 9763.77050 0.00000 9395.67160 -0.00100 9763.82540 -0.00040 9397.59600 -0.00050 9764.75820 -0.00060 9397.65400 -0.00060 9764.81600 -0.00170 9397.71260 0.00000 9766.74120 0.00020 9397.81660 -0.00040 9766.79870 -0.00010 9398.58640 0.00010 9766.84970 0.00060 9398.64720 0.00100 9768.77350 0.00020 9398.70060 0.00010 9768.82640 -0.00040 9398.75020 -0.00060 10142.64380 -0.00110 9398.80820 -0.00030 10142.75060 -0.00080 9400.73100 -0.00080 10143.58120 0.00120 9400.79050 -0.00020 10143.63170 -0.00020 9401.66440 0.00040 10143.68400 0.00020 9401.72400 0.00040 10143.74480 0.00160 9419.69910 0.00070 10143.79840 -0.00090 9419.74950 0.00080 10144.61900 0.00010 9420.57270 0.00050 10144.67400 -0.00070 9420.63420 0.00200 10144.73460 0.00030 9421.62380 0.00150 10144.78560 -0.00080 9421.72720 0.00090 10145.55520 -0.00090 9422.61070 0.00050 10145.60780 0.00040 9422.66130 0.00090 10145.66500 -0.00150 10145.72280 -0.00060 11945.64280 -0.00010 10145.77260 -0.00070 11945.69390 0.00080 10147.58980 -0.00010 11945.74950 -0.00080 10147.64720 -0.00010 11945.80950 0.00040 10147.69680 -0.00070 12389.53740 0.00100 10148.58160 0.00020 12389.58770 0.00130 10148.63440 -0.00040 12389.64100 -0.00120 10148.68580 0.00040 12392.55550 -0.00190 10148.74230 -0.00150 12392.61540 0.00060 10879.55000 0.00180 13047.07710 0.00050 10879.60870 0.00070 13047.12740 -0.00060 10879.66320 0.00090 13063.07180 0.00090 10879.71320 0.00060 13063.12330 -0.00040 10879.77270 0.00230 13110.99540 0.00160 11933.66140 -0.00060 13141.99740 0.00020 11933.71350 0.00070 13142.98350 -0.00060 11933.76590 0.00000 13280.18050 0.00160 11933.82520 -0.00060 13280.23590 0.00090 11934.53570 0.00040 13331.07570 0.00090 11934.65050 0.00040 13331.13320 0.00050 11934.70090 0.00070 13331.18370 0.00060 11934.81660 0.00040 13331.23700 -0.00010 11934.86690 -0.00050 13336.07390 -0.00150 11935.52470 -0.00200 13336.13590 0.00130 11935.58440 -0.00130 13336.18580 -0.00010 11935.63740 0.00030 13336.23790 -0.00040 11935.68900 -0.00040 13345.03670 -0.00060 11935.80200 -0.00260 13345.08790 0.00030 11936.62390 -0.00030 13379.05470 -0.00130 11936.68150 0.00090 13379.11720 0.00120 11936.73910 -0.00090 13379.16920 -0.00090 11936.79190 0.00030 13379.22080 0.00040 11936.84410 0.00050 13379.27800 -0.00020 11936.90200 -0.00120 13393.12670 0.00010 11937.50950 0.00010 13394.06150 0.00030 11937.56120 0.00000 13394.11710 -0.00070 11937.61330 0.00020 13394.17620 -0.00080 11937.67190 -0.00060 13394.22800 -0.00050 11937.72890 0.00030 13410.99300 -0.00080 11937.77900 0.00040 13411.04460 -0.00010 11937.83320 -0.00150 13411.10330 0.00000 11937.89430 0.00020 13411.16160 0.00080 11940.52690 -0.00040 13411.21120 0.00020 11940.69250 0.00150 13411.26370 -0.00190 11940.74830 -0.00150 13411.98080 0.00010 11943.55120 0.00010 13425.01360 0.00230 11943.60390 -0.00090 13425.06420 -0.00110 11943.66540 0.00076 13425.11620 0.00050 11943.76970 0.00060 13442.04750 -0.00030 11944.65450 -0.00040 13618.26590 -0.00080 11944.70670 0.00110 13633.21150 -0.00020 11944.75950 0.00060 13644.15100 0.00030 11944.81810 -0.00060 13644.20360 -0.00090 11944.87350 0.00030 13644.26650 0.00200 11945.52930 0.00100 13644.31740 -0.00090 11945.58790 -0.00020 13709.06890 0.00070