在疏散星團NGC663的兩個星野中搜尋短時間內能看到光度變化的變星

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(1)National Taiwan Normal University Department of Earth Sciences. M.Sc. Thesis. A search for variable stars with small variations in two selected fields toward the open cluster NGC 663. Ching-Yu Shao Advisor：Hsieh-Hai Fu, Ph.D.. August, 2010 I.

(2) 摘. 要. 疏散星團中的變星數量統計，可以用來認識與瞭解星團的演化狀態。本研究針對疏散星團 NGC663 中的兩個星野，使用短時間曝光、持續一小時的觀測，搜尋在數分鐘至數小時尺度內能看到光度變化的變星，作為初步統計之用。觀測在 2003 年 8 月 9 日晚上進行，使用國立中央大學鹿林山天文台 1 公尺望遠鏡配置 V 光度濾鏡，每幅影像曝光 1 分鐘，連續拍攝，持續約一小時，星野一得到 57 幅影像及星野二得到 63 幅影像。每幅影像經過扣除暗電流、平場修正等標準程序，再以美國國家光學天文台所發展之天文影像處理軟體 IRAF 之 DAOFIND、PHOT、點瀰散函數(PSF)進行擬合，獲得每顆恆星的座標與儀器星等。每幅影像中的恆星儀器星等，以參考星等(van den Bergh and de Roux, 1978)進行線性回歸擬合，轉換成 V 星等。兩個區域中可供分析的 V 星等範圍分別是 12.5～19 以及 13.5～18.5。完成所有 57 幅與 63 幅影像之星等校準後，繪製每顆恆星的光度變化曲線(light curve，簡稱光曲線)，以肉眼檢視每顆恆星之光曲線，找出亮度有變化的恆星。本研究在疏散星團 NGC 663 及其附近區域中的兩個星野（星野一與星野二），一共發現 9 顆疑似變星，其中 4 顆恆星亮度呈現持續上升或下降的趨勢，其他 5 顆的亮度則屬於不規則變化。依據文獻，在 NGC 663 中已經發現了一些變星，在本研究的兩個區域中有 16 顆已知變星。其中一顆的光度在本次一小時的觀測中呈現變化。由統計的角度來看，依據文獻(Pigulski et al. 2001)，在觀測得到的 715 顆恆星中確認了 24 顆變星，比例為 3.36 %。而本研究中，兩個星野可供分析的共有 1192 顆恆星，已知變星佔的比例為 1.34%，將疑似變星也列入統計，那麼變星的比例為 2.10%，略低於 3.36%。所以在疏散星團中搜尋短時間有變化的變星的可行性是相當高的。. I.

(3) Abstract. The state of evolution of a star cluster could be studied by the percentage of variable stars in the cluster. In this work, two regions toward an open cluster NGC 663 are observed with V filter using one meter telescope (LOT) at Lulin observatory of National Central University on the night, August 9, 2003. The goal was trying to find the variable stars with variation in minutes to hours. There are 57 and 63 frames obtained for Region 1 and Region 2 respectively. The magnitude of a star in each frame was derived by data reduction and magnitude calibration. The completeness of V magnitude reveals the useful magnitude range, 12.5 ~ 19 and 13.5 ~ 18.5, for searching variable stars in region 1 and region 2, respectively. Light curves of the stars were plotted and used to find out the brightness change in the interval of about an hour. There are 9 suspected variable stars found in both two regions of NGC 663. The brightnesses of four stars show a continuous rise or fall, other stars are irregular. There are several variable stars in NGC 663 presented in other’s studies. 16 known variable stars are located in the two regions. In the observations, one of the known stars shows a change in the light curve but the others do not. The percentage of variable stars (16) to total stars (1192) is about 1.34%. If the suspected variables (9) are included, the percentage will be 2.10 %. The value is slightly less than the percentage, 3.36 %, derived from the number of variables (24) and detected stars (715) given by Pigulski et al. (2001). This result implies that it is possible to use the short-term light variation for variable stars survey in the stellar clusters. II.

(4) Content 1. Introduction …………………………………………………………….……. 01 1.1 The Variable Stars in Open Cluster …...…...…………………………… 01 1.2 Open Cluster NGC 663 ……………………...…………………………… 01 1.3 Variable Stars …...………………………………………………………... 03. 2 Observations and Data Reduction …………………………………...……… 05 2.1 Observations …..………………………………………………………….. 05 2.2 Data Reduction .…......……………………………..…………................... 08 3. Magnitude Calibration ……..…………….………………………………….. 11. 4. Results …..……………………………….……………………………………. 19 4.1 Completeness of V magnitude ….……………………………………….. 19 4.2 Light Curves of the Two Regions ……………………..………………… 21 4.3 Suspected Variable Stars …..…………………………………………….. 22. 5 Conclusion and Discussion …………………………………………………... 30 Reference …………………………………………………………………………. 34 Appendix 1. Coordinate Transformation …….…….……..………….….…….. 35. Appendix 2. Plots of magnitude calibration …………………………………... 39. Appendix 3. The data of observation for NGC 663 ……………….………….. 50. Appendix 4. The distribution of stars for NGC 663 ……………….…………. 57. Appendix 5. Light curve of all stars ..………………………………………….... Appendix 6. The IDL source code for equation of coordinate transformation ..... 89. Appendix 7. The IDL source code for equation of magnitude calibration ….. 94. Appendix 8. The IDL source code for plot light curve …...…………………... 100. III. 65.

(5) List of Figure Fig. 1. Position of NGC 663 in the Cassiopeia(Plot with Stellarium 10.2) ....... 02. Fig. 2. A 30′ ×30′ fragment of the POSS Ⅰ plate centered on NGC 663. Two overlapped areas cover the field for searching variable stars ….…….. 06. Fig. 3. Image of NGC 663 in Region 1 using V filter with LOT …….…..……. 07. Fig. 4. Image of NGC 663 in Region 2 using V filter with LOT ...…….…........ 08. Fig. 5. The stars distributions in Region 1 of NGC 663 …..………………….. 09. Fig. 6. The stars distributions in Region 2 of NGC 663 …..….……………….. 10. Fig. 7. Chart for stars having photographic photometry by van den Bergh and de Roux (1978). The circle has a radius ~ 250″ …………............... 11. Fig. 8. A diagram for distributions of reference stars labeled with open 14 circles and numbers for this work in Region 1 ………………………... Fig. 9. A diagram for distributions of reference stars labeled with open circles and numbers for this work in Region 2 ……………………….. 15. Fig. 10. One plot of the equation of magnitude calibration for Region 1 .…... 16. Fig. 11. Plot of the equation of magnitude calibration for Frame 20 in Region 2 ……………..………………………………………………….. 17. Fig. 12. Histogram for star counts relative to the interval of magnitude in Region 1 …...……………………………………………………………. 20. Fig. 13. Histogram for star counts relative to the interval of magnitude in Region 2 ……………………………………………….………………... 21. Fig. 14. The light curves of first forty stars with number, mean of magnitude and standard error in Region 1. The unit of abscissa is exposure time in hour……………………………..……...……………………….. 22. Fig. 15 Light curves of suspected variable stars in Region 1 ……..…………. 23 Fig. 16 Light curves of suspected variable stars in Region 2 ………………... 24 Fig. 17. A diagram of the observed field with all stars detected by CCD in Region 1. Suspected variable stars are marked with open circles and numbers …………………………………................................................ 25 IV.

(6) Fig. 18. A diagram of the observed field with all stars detected by CCD in Region 2. Suspected variable stars are marked with open circles and numbers ……………………………….................................................... 26. Fig. 19. A diagram of with all stars detected by CCD in Region 1. The confirmed variable stars are marked with open circles and numbers, the suspected variable stars with open diamonds and numbers ……………………………………………….…………........... 28. Fig. 20. A diagram of with all stars detected by CCD in Region 2. The confirmed variable stars are marked with open circles and numbers, the suspected variable stars with open diamonds and numbers ……………................................................................................ 29. Fig. 21. Plot of average V magnitudes vs. standard errors in Region 1 …….. 32. Fig. 22. Plot of average V magnitudes vs. standard errors in Region 2 …….. 32. V.

(7) List of Tables Table 1. The Observing log for Region 1 ……..……………………………….. 06. Table 2. The Observing log for Region 2 ………..…………………………….. 07. Table 3. List of standard stars derive from van den Bergh et al. 1978 in Region 1 ………………………………………………………………... 12. Table 4. List of standard stars derive from van den Bergh et al. 1978 in Region 2 ………………………………………………………………... 13. Table 5 a, b, and σ for each frames in Region 1 ……………………………… 17 Table 6 a, b, and σ for each frames in Region 2 ……………………………… 18 Table 7. The star counts relative to the interval of magnitude in Region 1 … 19. Table 8. The star counts relative to the interval of magnitude in Region 2 … 20. Table 9 Data of suspected variable stars in Region 1 and 2 …………………. 23 Table 10 Variable stars confirmed by literatures or GCVS in Region 1 ……... 27 Table 11 Variable stars confirmed by literatures or GCVS in Region 2 ……... 28. VI.

(8) Chapter 1 Introduction. 1.1 The variable stars in open clusters The first step of the open clusters programs at Institute of Earth Sciences, NTNU is the search for variable stars with luminosity changing quickly in the range of minutes to an hour toward the open cluster NGC 663. Variable stars are commonly found in open clusters, but the percentage of the type of variable stars in an open cluster is studied rarely. Many variable stars exist in the young and old open clusters, because stars are unstable in the beginning and the end stage of its life. Open clusters are groups of hundreds to thousands of stars held together by mutual gravitational force, and they are useful tools for studying stellar evolution because they formed from the same molecular cloud. The star members are considered with the same age and chemical compositions. The age of open clusters is in the range of a few million years to billion years, and that is typically less than 100 million years for young open clusters. In the later stage of the stellar evolution, the stars will leave the main sequence and the surface will expand because of heat inequilibrium inside. However, some kinds of variable stars, such as delta Scuti stars, are located at the area crossing with the main sequence in the H-R diagram.. 1.2 Open cluster NGC 663 The young open cluster NGC 663 with many stars of V magnitude between 12. 1.

(9) and 20 is located in the Cassiopeia (Fig. 1), R.A.(2000): 01h 46m 09s and DEC.(2000): + 61˚ 14′ 06″ (l = 129˚.46, b = +0˚.99). It lies in the Perseus arm of our Milky Way Galaxy and also in the center of the association Cas OB8. The distance of NGC 663 is estimated to be 2.1 kpc and the age is about 25 million years (Fabregat et al. 2004). Its apparent diameter is about 16 arc minutes (Dias et al. 2002).. N. NGC 663. Fig. 1, Position of NGC 663 in the Cassiopeia (Plot with Stellarium 10.2).. NGC 663 was usually the target for many photometric studies. For examples, photoelectric photometry of stars was obtained by Hoag et al. (1961), published by McCuskey et al. (1964), and UBV photometry was given by van den Bergh et al. (1978). CCD uvbyβ photometry was presented by Fabregat et al. (2004). The distance and the age of NGC 663 were confirmed precisely in the literatures.. 2.

(10) Why the young open cluster NGC 663 was selected as a target for searching variable stars with brightnesses changing notably in an hour. First, many variable stars in NGC 663 were recorded in the literatures. For examples, Pietrzynski (1996, 1997) discovered 7 variable stars, 2 Be stars, 2 probable RR Lyrae variables, 1 background β Cepheid star and 2 eclipsing stars. Pigulski et al. (2001) presented 24 variable stars with 19 new variables and 5 stars were confirmed. Second, lots of photometric data were presented in literatures that could be used for the magnitude calibration. The diameter of NGC 663 is about 16 arc minutes. The image field of the CCD equipped with one-meter telescope of Lulin Observatory is about 11 arc minutes, and the two selected fields roughly covered most area of NGC 663.. 1.3 Variable Stars Variable stars, especially their location in the H-R diagram, are the good tool for studying the stellar structure and evolution. The variation of light curve is usually used as a character for classification of variable stars: regular, semi-regular and irregular variables. According to observable properties, there is also a criterion for classification, intrinsic and extrinsic variables. The brightness of the intrinsic variables, divided into pulsating stars and eruptive stars, is changed within the stars themselves, and they provide a wealth of information about the internal structure of stars and models of stellar evolution. The pulsating variable stars are also divided into many sub-types, Cepheids, RR Lyrae variables, Mira stars, etc. The eruptive variables are divided into novae, supernovae, dwarf novae, etc. The most extrinsic variables are eclipsing binary stars: Algol variables, Beta Lyrae variables and W Ursae Majoris variables. 3.

(11) The periods of light curves of some variable stars are short. The time scale is about several days to a few hours. For examples, the periods of RR Lyra variables are several hours to a day or more, the periods of Delta Scuti variables are 0.01 - 0.2 days, and the brightness of SX Phoenicis variables changes every 1 to 2 hours. The literatures searching for variable stars show that there are rare variable stars with brightnesses varied within a short time range. For this work, it searches for the variables with light variations notable in an hour. The percentage of variables will be estimated from a simple statistical method.. 4.

(12) Chapter 2 Observations and Data Reduction. 2.1 Observations All images of NGC 663 were carried out at Lulin Observatory of National Central University with the Lulin one-meter telescope (LOT) in Taiwan. A Princeton Instruments VersArray, 1300B (PI 1300B) CCD, is equipped on the focus plane of LOT (f/8). The size of the CCD was 1340 × 1300 pixels with one pixel corresponding to 0.515″; the field of view was 11.50′ × 11.15′. At 1 MHz readout speed, the CCD readout noise is 8 electrons rms. the working temperature on the surface of the chip was set to – 50 ℃. The observations were made on the night, August 9, 2003. Because the diameter of NGC 663 (16 arc minutes) is larger than CCD field on LOT (11.50 × 11.15 arc minutes), the cluster was divided into two regions. These two regions and the overlapped area are shown in Fig. 2. The CCD images of Region 1 and Region 2 are shown in Fig. 3 and Fig. 4, respectively. In order to search for small-timescale variable stars, the exposure times were controlled to one minute. 57 frames with one-minute exposure were taken in Region 1 and 63 frames were taken in Region 2. All frames were taken using the V filter. A number of bias, dark and flat frames were also taken during the observing runs. The Observing logs are given in Tables 1 and 2. Stars with photometry obtained by van den Bergh et al. (1978) were used as standards for magnitude calibration.. 5.

(13) Fig. 2, A 30′ ×30′ fragment of the POSS Ⅰ plate centered on NGC 663. Two overlapped areas cover the field for searching variable stars.. Table 1, The observing log for Region1. Frame 1 2 3 4 5 7 8 9 10 11 12 13 14 15 16 17 18 19 20. Time (UT) 18:05:25 18:06:29 18:07:32 18:08:35 18:09:39 18:12:49 18:13:52 18:14:55 18:15:59 18:17:02 18:18:06 18:19:09 18:20:13 18:21:16 18:22:20 18:23:23 18:24:26 18:25:30 18:26:34. Frame 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39. Time (UT) 18:27:37 18:28:41 18:29:44 18:30:48 18:31:52 18:32:55 18:33:59 18:35:02 18:36:06 18:37:09 18:38:12 18:39:15 18:40:19 18:41:22 18:42:26 18:43:29 18:44:33 18:45:36 18:46:40. 6. Frame 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 58 59. Time (UT) 18:47:43 18:48:46 18:49:49 18:50:53 18:51:56 18:52:59 18:54:03 18:55:07 18:56:10 18:57:13 18:58:17 18:59:21 19:00:24 19:01:28 19:02:31 19:03:34 19:04:38 19:10:32 19:11:35.

(14) Table 2, The observing log for Region 2. Frame 1 2 3 4 5 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22. Time (UT) 19:19:22 19:20:25 19:21:28 19:22:31 19:23:35 19:26:46 19:27:49 09:28:52 19:29:56 19:31:00 19:32:04 19:33:07 19:34:10 19:35:14 19:36:18 19:37:21 19:38:25 19:39:28 19:40:31 19:41:35 19:42:38. Frame 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43. Time (UT) 19:43:42 19:44:45 19:45:48 19:46:52 19:47:55 19:48:58 19:50:02 19:51:06 19:52:10 19:53:13 19:54:17 19:55:20 19:56:24 19:57:28' 19:58:31 19:59:34 20:00:38 20:01:42 20:02:45 20:03:49 20:04:52. Frame 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64. Time (UT) 20:05:55 20:06:59 20:08:03 20:09:06 20:10:10 20:11:13 20:12:16 20:13:20 20:14:24 20:15:28 20:16:32 20:17:35 20:18:38 20:19:42 20:20:45 20:21:50 20:22:53 20:23:57 20:25:00 20:26:04 20:27:07. Fig. 3, Image of NGC 663 in Region 1 using V filter with LOT (Field 11.5′) 7.

(15) Fig. 4, Image of NGC 663 in Region 2 using V filter with LOT (Field 11.5′). 2.2 Data Reduction All images were processed using MaxIm DL and IRAF. During the observing runs, the bias, dark and flat frames were taken by Chih-Kang Wu. The Cyanogen MaxIm DL Version 3.0 package was applied to subtract the bias, dark and to correct the flat-field. The cleaned images were then used for the reduction process performed with IRAF (NOAO) routines. The stellar instrumental magnitude and position of each star were derived by DAOFIND, PHOT, Point Spread Function (PSF) fitting and ALLSTAR tasks of IRAF DAOPHOT Ⅱ package (Stetson 1987). The PSF was obtained for each frame using several uncontaminated stars. The best frame from each region was used to make a reference list. After careful inspection of the frames, 8.

(16) all spurious stars were removed. The resulting reference lists consist of 1045 stars in Region 1 and 720 stars in Region 2. The detailed maps of two fields are shown in Fig. 5 (Region 1) and Fig. 6 (Region 2), respectively.. Fig. 5, The stars distributions in Region 1 of NGC 663. 9.

(17) Fig. 6, The stars distributions in Region 2 of NGC 663. 10.

(18) Chapter 3 Magnitude Calibration. For each frame, the magnitude calibration is executed by the method of linear regression with the photographic magnitude taken from van den Bergh and de Roux (1978). The standard stars used by this work are charted in Fig. 7.. Fig. 7, Chart for stars having photographic photometry by van den Bergh and de Roux (1978). The circle has a radius ~ 250″. 11.

(19) The standard stars from van den Bergh et al. (1978) were listed in Tables 3 and 4 with serial number for this observation in Region 1 and Region 2, respectively. In these two fields, there are 59 stars in Region 1 and 21 stars in Region 2, and the distributions of standard stars in Region 1 and Region 2 are shown in symbols of open circle in Fig. 8 and Fig. 9, respectively. However, some stars must be excluded from the list for the following reasons. In Region 1, stars No. 675, 703, 706, 841 and 916 are confirmed variable stars (Pietrzynski 1997, Pigulski et al. 2001). No. 514, 669, 741, 750 and 861 are too bright for the use; the magnitudes of stars No. 424, 431, 432, 646, 698, 844 and 896 are fitted no good or nothing because these stars are very close to neighbor stars; brightnesses of No. 378, 484, 574, 579, 721, 810, 840, 901, 968 and 989 change irregularly. In Region 2, star No.162 is confirmed as a variable star (Pigulski et al. 2001); No. 94 and 136 are too bright; brightnesses of No. 14, 31, 37, 111, 113, 126 and 130 vary irregularly. Finally, 32 stars in Region 1 and 11 stars in Region 2 are chosen as reference or standard stars for this work.. Table 3, List of standard stars derived from van den Bergh et al. 1978 in Region 1 No. Num. 345 377 378 380 394 424 431 432 452. *1 Mag.. 247 274 275 246 245 243 244 276 242. X (V) (pixels). 12.76 14.78 15.31 15.14 12.87 14.40 15.12 14.02 14.54. Y X *1 Mag. note No. Num. (pixels) (V) (pixels). 594.387 725.473 619.577 962.208 620.177 1044.957 623.145 721.176 641.200 665.746 674.242 658.888 685.277 658.109 686.145 1113.495 709.161 598.232. *2. *2 *2 *2. 706 721 741 750 765 774 780 810 811. 12. 255 203 256 232 231 230 204 205 227. 10.43 967.518 14.32 981.919 12.42 997.416 12.26 1003.671 14.50 1019.686 12.80 1029.491 14.62 1034.720 13.55 1053.630 14.93 1053.635. Y note (pixels) 971.619 529.437 960.247 712.540 761.740 788.467 526.747 551.084 695.903. *2 *2 *2 *2. *2.

(20) 484 509 514 516 569 573 574 576 579 589 597 614 627 644. 277 241 248 240 249 272 273 250 237 281 236 251 235 254. 15.28 15.16 11.03 13.86 14.95 14.17 14.81 13.51 14.30 14.12 12.24 13.53 14.65 15.26. 737.168 1125.019 773.843 614.309 782.184 861.071 785.614 626.734 840.220 922.823 844.037 1004.546 845.601 1041.510 846.844 963.216 848.247 744.640 859.176 1163.082 867.089 820.771 885.085 923.192 891.482 832.412 904.420 979.475. *2 817 840 *2 841 844 861 864 *2 868 871 *2 892 896 901 902 916 945. 257 207 228 229 206 258 270 226 225 224 259 260 223 261. 13.49 1058.509 1019.435 15.23 1088.062 616.825 11.89 1088.188 754.294 14.77 1090.218 773.615 11.58 1109.273 585.854 15.11 1109.818 927.136 14.34 1114.127 1131.818 15.12 1121.497 705.566 14.99 1141.530 747.531 14.64 1146.098 794.488 15.36 1150.839 1056.849 12.79 1154.400 1079.440 13.14 1169.578 833.733 14.56 1200.087 1083.521. 646 658 669 675 698 701 703. 202 201 252 233 253 271 234. 14.32 15.07 12.21 12.12 14.94 14.82 12.67. 907.833 551.897 926.613 476.421 936.462 902.630 943.796 728.799 963.562 915.873 965.042 1164.320 966.400 806.041. *2 950 961 *2 968 *2 977 *2 984 989 *2. 222 221 208 262 220 211. 15.16 1206.833 835.543 12.75 1218.290 997.639 14.05 1224.622 615.690 *2 13.52 1232.967 1077.660 12.50 1237.385 1011.905 13.82 1240.773 810.291 *2. *2 *2 *2 *2. *2 *2 *2. *1, Number from van den Bergh et al. (1978) *2, Not used to magnitude calibration due to variable star, too bright, overlap with near stars….. Table 4, List of standard stars derived from van den Bergh et al. 1978 in Region 2 Star Num. 1046 1052 1059 1065 1070 1076 1082 1129 1139 1145. *1 Mag.. 221 208 262 220 211 263 268 219 212 267. X (V) (pixels). 12.75 14.05 13.52 12.50 13.82 15.21 14.07 13.50 11.87 14.52. Y X *1 Mag. note Star Num. (pixels) (V) (pixels). 104.026 931.192 112.195 549.269 118.348 1011.288 123.079 945.555 127.41 743.922 137.084 1056.246 139.366 1115.653 189.899 944.249 214.018 836.691 221.947 1128.048. *2. *2 *2 *2. 1156 1158 1160 1171 1175 1181 1207 1231 1244 1263. 13. 266 209 218 265 264 217 213 216 215 214. Y note (pixels). 13.28 234.327 1118.764 13.95 234.762 628.409 14.84 236.084 943.788 14.10 246.582 1068.882 14.44 249.357 1054.374 11.82 255.099 962.175 11.70 297.989 899.751 13.52 320.659 1003.503 13.26 330.83 994.662 14.96 360.695 902.156. *2 *2 *2 *2 *2 *2.

(21) 1146. 210. 14.58 222.022 704.998. *1, Number from van den Bergh et al. (1978) *2, Not used to magnitude calibration due to variable star, too bright, overlap with near stars….. Fig. 8, A diagram for distributions of reference stars labeled with open circles and numbers for this work in Region 1.. 14.

(22) Fig. 9, A diagram for distributions of reference stars labeled with open circles and numbers for this work in Region 2.. The equation of magnitude calibration for each frame is given as follows: V = a +b v where V is the reference magnitude, v is the instrument magnitude, and a, b are fitting constants. The standard error, σ, is defined as.  .  V  v  . n1 2. There are 58 frames in Region 1 and 63 frames in Region 2. The constants, a and b, and the standard error, σ, for each frame in Region 1 and that in Region 2 are listed in the Table 5 and 6 respectively. The mean of standard error of V magnitude is usually about 0.008 in both regions. The typical plots of equation of magnitude 15.

(23) calibration for a frame is shown in Fig. 10.The plots of equations of magnitude calibration for Region 1 and that for Region 2 are shown in the Appendix 2.. Fig. 10, One plot of the equation of magnitude calibration for Region 1. There is probably abnormal for the results of linear regression on frame 20 in Region 2 (show on Fig. 11), because the values of standard errors of V magnitude are 0.011, slightly larger than others. One possibility is that the qualities of images are not good as others. Only 7 standard stars can be used on frame 20 because tracking of telescope was not accurate. However, the time interval of the frame 20 for all observations is about 1.56%, and the influence can be ignored in this work.. 16.

(24) Fig. 11, Plot of the equation of magnitude calibration for Frame 20 in Region 2 Table 5 a, b, and σ for each frame in Region 1 frame. a. b. σ. frame. a. B. σ. frame. a. b. σ. 1 2 3 4 5 7 8. 1.896 1.911 2.004 1.975 2.087 1.651 1.676. 1.007 1.007 1.002 1.004 0.997 1.014 1.013. 0.006 0.006 0.006 0.007 0.007 0.005 0.006. 21 22 23 24 25 26 27. 1.966 1.935 1.852 1.927 1.973 1.993 2.076. 1.004 1.006 1.012 1.007 1.006 1.004 0.999. 0.007 0.007 0.006 0.006 0.006 0.007 0.007. 40 41 42 43 44 45 46. 1.936 1.830 1.853 1.975 1.858 2.036 2.019. 1.005 1.008 1.006 1.003 1.010 1.001 1.001. 0.006 0.006 0.006 0.006 0.006 0.008 0.008. 9 10 11 12 13 14 15 16 17 18. 1.47 1.544 1.738 1.777 1.873 1.875 1.956 1.858 1.758 2.002. 1.015 1.014 1.011 1.012 1.011 1.008 1.005 1.009 1.013 1.004. 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006. 28 29 30 31 32 33 34 35 36 37. 2.004 1.939 1.924 1.871 1.845 1.889 1.927 1.904 1.939 1.882. 1.004 1.008 1.008 1.010 1.012 1.008 1.009 1.008 1.006 1.009. 0.007 0.006 0.006 0.005 0.006 0.006 0.006 0.006 0.006 0.006. 47 48 49 50 51 52 53 54 55 56. 1.952 1.947 1.889 1.725 1.779 1.847 1.825 2.03 2.058 2.104. 1.005 1.004 1.010 1.012 1.011 1.008 1.011 1.009 1.002 0.997. 0.006 0.007 0.006 0.005 0.005 0.006 0.006 0.006 0.008 0.008. 17.

(25) 19 1.815 1.010 0.006 20 1.764 1.013 0.006. 38 39. 1.994 1.004 0.006 1.958 1.003 0.007. 58 59. 2.028 1.003 0.007 1.929 1.007 0.006. Table 6 a, b, and σ for each frame in Region 2 frame. a. b. σ. frame. A. b. σ. frame. a. b. σ. 1 2 3 4 5 7 8. 2.024 2.014 2.041 2.059 2.064 2.116 2.165. 0.982 0.982 0.980 0.982 0.980 0.980 0.982. 0.007 0.008 0.008 0.008 0.007 0.007 0.009. 23 24 25 26 27 28 29. 2.103 2.049 2.104 2.015 2.056 2.086 2.209. 0.981 0.982 0.980 0.981 0.980 0.981 0.979. 0.008 0.009 0.008 0.008 0.007 0.007 0.007. 44 45 46 47 48 49 50. 2.075 1.967 1.955 2.053 2.097 2.127 2.271. 0.982 0.978 0.981 0.978 0.978 0.978 0.962. 0.009 0.008 0.008 0.008 0.008 0.008 0.008. 9 10 11 12 13 14 15 16 17 18 19 20 21 22. 2.141 2.124 2.136 2.146 2.096 2.083 2.163 2.112 2.109 2.088 2.135 1.920 2.106 2.049. 0.982 0.981 0.978 0.977 0.980 0.981 0.981 0.982 0.979 0.978 0.979 0.995 0.980 0.980. 0.007 0.007 0.007 0.006 0.007 0.008 0.007 0.007 0.007 0.006 0.006 0.011 0.007 0.008. 30 31 32 33 34 35 36 37 38 39 40 41 42 43. 2.166 1.965 2.007 2.080 2.093 2.080 1.951 2.024 2.093 1.941 2.011 2.057 2.057 2.07. 0.981 0.980 0.984 0.979 0.979 0.979 0.981 0.982 0.980 0.982 0.979 0.980 0.979 0.979. 0.008 0.007 0.009 0.007 0.007 0.008 0.007 0.008 0.008 0.008 0.008 0.008 0.008 0.008. 51 52 53 54 55 56 57 58 59 60 61 62 63 64. 2.031 2.05 2.065 2.096 2.09 2.07 2.061 2.115 2.118 2.124 2.174 2.006 2.075 2.062. 0.979 0.979 0.977 0.977 0.977 0.978 0.979 0.977 0.977 0.977 0.985 0.979 0.977 0.979. 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.007 0.008 0.008 0.008 0.008 0.008. For each frame, the magnitude of each star is calculated from the equation of magnitude calibration. When the calibrated magnitude of each star for each frame is obtained, the light curve of each star is plotted.. 18.

(26) Chapter 4 Results. 4.1 Completeness of V magnitude The completeness is important for statistics of percentage of variable stars on the selected fields. The incompleteness in the data mainly comes from some stars, which are missed due to overlap with the other stars, or hidden under the shining spikes of bright stars in the image fitting process. Another reason is that the qualities of images are not good. The completeness of V magnitude in both Regions 1 and 2 is derived in terms of photometric data, the histograms of star counts at intervals of ΔV= 0.5. We have not incorporated a fake star routine into the photometry software to establish the completeness of V photometry, but it is suitable that V=12.5-19 in Region 1 and V=13 - 18.5 in Region 2 represent the completeness. The star counts in each interval are listed in Table 7 and 8, and the histograms are shown in Fig. 12 and 13, respectively.. Table 7, The star counts relative to V magnitude in Region 1 Magnitude Star count Magnitude Star count Magnitude Star count 10.0-10.4 10.5-10.9 11.0-11.4 11.5-11.9 12.0-12.4 12.5-12.9 13.0-13.4 13.5-13.9. 0 5 7 7 13 15 16 24. 14.0-14.4 14.5-14.9 15.0-15.4 15.5-15.9 16.0-16.4 16.5-16.9 17.0-17.4 17.5-17.9. 28 35 53 61 64 72 86 100 19. 18.0-18.4 18.5-18.9 19.0-19.4 19.5-19.9 20.0-20.4 20.5-20.9 21.0-21.4 21.5-21.9. 119 170 113 52 4 1 0 0.

(27) Fig. 12, Histogram for star counts relative to V magnitude in Region 1. Table 8, The star counts relative to V magnitude in Region 2 Magnitude Star count Magnitude Star count Magnitude Star count 11.5-11.9 12.0-12.4 12.5-12.9 13.0-13.4 13.5-13.9 14.0-14.4. 3 9 9 10 17 19. 14.5-14.9 15.0-15.4 15.5-15.9 16.0-16.4 16.5-16.9 17.0-17.4. 18 45 42 48 48 72. 20. 17.5-17.9 18.0-18.4 18.5-18.9 19.0-19.4 19.5-19.9 20.0-20.4. 65 91 70 80 64 44.

(28) Fig. 13, Histogram for star counts relative to V magnitude in Region 2. 4.2 Light Curves of the Two Regions The light curves of first forty stars in Region 1 of NGC 663 are shown in Fig. 14. The ordinate shows the magnitude difference. The light curve for each star is produced by the following steps: 1. Take the average magnitude over all frames. 2. Take difference between the magnitude of each frame and the average magnitude. 3. Plot the magnitude difference (ordinate) against the number of frame (i.e. time, abscissa). The light curve of each star will be inspected very carefully. The suspected variable stars will be picked out if its light variation is apparently or regularly rising up or falling down.. 21.

(29) Fig. 14, The light curves of first forty stars with number, mean of magnitude and standard error in Region 1. The unit of abscissa is exposure time in hour.. 4.3 Suspected Variable Stars With inspection of all light curves, 10 suspected variable stars are picked out, 6 in Region 1 and 4 in Region 2. The data of the 10 suspected variable stars are listed in Table 9 and their light curves are shown in Fig. 15 (Region 1) and Fig. 16 (Region 2). Locations of these stars are marked in Fig. 17 and Fig. 18.. 22.

(30) Table 9, Data of suspected variable stars in Region 1 and 2 Region 1 No. X(Pixel). Region 2. Y(Pixel) Mag.(mean) No. X(Pixel). 464 719.259 1194.731 534 806.532 889.039 567 837.599 222.562 706 967.518 971.619 792 1042.956 859.377 828 1072.009 799.122. 18.74 18.28 14.31 17.60 18.18 16.39. 1120 1563 1709 1781. Y(Pixel). 186.347 1097.877 819.901 1031.799 1086.156 1207.100. 308.566 93.420. Fig.15, Light curves of suspected variable stars in Region 1. 23. Mag.(mean) 16.15 17.88 16.50 16.61.

(31) Fig. 16, Light curves of suspected variable stars in Region 2. 24.

(32) Fig. 17, A diagram of the observed field with all stars detected by CCD in Region 1. Suspected variable stars are marked with open circles and numbers. 25.

(33) Fig. 18, A diagram of the observed field with all stars detected by CCD in Region 2. Suspected variable stars are marked with open circles and numbers.. The variable stars in NGC 663 have been surveyed by many research workers (e.g. Pietrzynski 1996, 1997; Pigulski et al. 2001). The whole region of NGC 663 covered roughly larger than the survey area of this work. 7 variable stars are found by Pietrzynski (1997), 19 variable stars by Pigulski et al. (2001), and also a few variable stars recorded in GCVS (General Catalogue of Variable Stars). There are 12 known variable stars in Region 1 and 4 stars in Region 2. Totally 16 stars are located in our observed field. The diagrams combining known and suspected variable stars are shown in Fig. 19 and Fig. 20. Their data are shown in Table 10 and 11. By 26.

(34) double check, one of the suspected variable stars, No. 567, is a known variable star (Pigulski et al. 2001), thus there are actually 5 suspected variable stars in Region 1.. Table 10, Variable stars confirmed by literatures or GCVS in Region 1 No. GCVS. P1. P2. X(pixel) Y(pixel). 286 553 567 620 675 703 706. V0986 ----V0985 V0984 --V0983. --v4 ----v5 -----. --W4 W125 --W6 W14 W21. 507.887 823.571 832.386 886.942 943.796 966.400 967.518. 340.026 765.028 227.454 569.816 728.799 806.041 971.619. 12.07(0.05Ic)Rc --11.04(0.04Ic)Rc 0.194047 14.25(0.11Ic)Rc 0.5760 9.85(0.36Ic)Rc --11.66(0.42Ic)Rc --12.66(0.15Ic)Rc --10.34(0.35Ic)Rc ---. 736 V0982 753 --767 --841 V0980 916 V0979. -----------. W8 W41 W79 W10 W51. 993.311 1009.739 1021.747 1088.188 1169.578. 767.580 498.066 429.746 754.294 833.733. 11.90(0.12Ic)Rc 0.67298 14.33(0.03Ic)Rc 0.6698 14.12(0.03Ic)Rc 1.3077 11.44(0.15Ic)Rc --12.85(0.10Ic)Rc ---. 27. Mag.(Range). Period(d).

(35) Fig. 19, A diagram of with stars detected by CCD in Region 1. The confirmed variable stars are marked with open circles and numbers, the suspected variable stars with open diamonds and numbers.. Table 11 Variable stars confirmed by literatures or GCVS in Region 2 No. GCVS. P1. P2. X(pixel). Y(pixel). V0978 V0977 V0976 V0974. --v6 -----. --W92 W93 ---. 165.740 253.589 297.989 530.637. 784.559 895.400 899.751 890.498. 1106 1178 1207 1360. 28. Mag.(Range). Period(d). 11.11(0.25Ic)Rc --10.23(0.20Ic)Rc 0.194047 11.58(0.20Ic)Rc 0.5760 12.09(0.10Ic)Rc ---.

(36) Fig. 20, A diagram of with stars detected by CCD in Region 2. The confirmed variable stars are marked with open circles and numbers, the suspected variable stars with open diamonds and numbers.. 29.

(37) Chapter 5 Conclusion and Discussion. In this work, we try to discover the variable stars with light variations within an hour. It is the first step of the open clusters programs at NTNU. Therefore, the light curves of all stars in two regions are plotted, including the members of NGC 663 and the field stars. The number of variable stars and suspected variable stars can be used to calculate the percentage of variable stars in the two fields of the cluster NGC663. The suspected variable stars in this work are not listed in literatures and GCVS. In Fig. 15, the light curves of star No. 464 and No. 792 show slow decrease; No. 705 vibrate notably around the later exposure time; No. 534 has the obvious difference between the first half and second half of the light curve; the light curves of No. 828 firstly fall and then rise above average. In Fig. 16, star No. 1709 and No. 1563 are almost considered as variable stars based on that their light curves fall or rise obviously. The light curve of star No. 1781 looks like a sine wave with a small amplitude of 0.05 mag. Furthermore, the variation of the light curves of star No. 1120 has gone down continuously. As mentioned above, it reveals the light variations within an hour can be detected for variable stars in open clusters. But the variable stars with the longer period cannot be found in the period of an hour, because the brightness variation should be very small, undetectable in this work. The average standard error of V magnitude is about 0.01 ~0.04, the amplitude of light curve for a longer period will not be noticeable from our one-hour observation. 30.

(38) The analysis ranges of V magnitude are derived from the plot of average V magnitudes vs. standard errors, ‹σ›, (shown in Fig. 21 and 22). In Region 1, according to the plots, ‹σ› in different ranges of V magnitude are ‹σ›~ 0.01 – 0.02 for V = 12 – 16, ‹σ› ~ 0.04 for V = 16 – 18, ‹σ› ~ 0.05 for V = 19. The limiting magnitude for analysis reaches down to about 19 magnitude with σ = 0.05. In Region 2, ‹σ› in different ranges of V magnitude are ‹σ›~ 0.01 – 0.02 for V = 13 – 16 ‹σ›~ 0.04 for V = 16 – 18 ‹σ›~ 0.05 for V = 18.5. The limiting magnitude for analysis reaches down to about 18.5 magnitude with σ = 0.05.. 31.

(39) Fig. 21, Plot of average V magnitudes vs. standard errors in Region 1. Fig. 22, Plot of average V magnitudes vs. standard errors in Region 2. 32.

(40) Statistically, in Region 1, 736 useful stars for completeness and 12 variables stars found from literatures, the number ratio for total 736 stars is about 1.63 %, and the ratio for 5 suspected variable stars is 0.68 %. In Region 2, the ratio of 4 variables stars to total 456 useful stars is roughly 0.88 %, and the ratio for 4 suspected variable stars is 0.88 %. In two regions, there are 1192 stars in total. Among them, there are 16 variable stars and 9 suspected variable stars. The percentage of variable stars to total stars is about 1.34%. If the suspected variables are included, the percentage will be 2.10 %. The value is slightly less than the percentage, 3.36 %, derived from the number of variables (24) and detected stars (715) given by Pigulski et al. (2001). This result implies that it is possible to use the short-term light variation for variable stars survey in the stellar clusters .. 33.

(41) Reference. Dias, W. S., Alessi, B. S., Moitinho, A., & Lépine, J. R. D., 2002, A&A, 389, 871. Fabregat, J., & Capilla, G., 2005, MNRAS, 358, 66. Hoag, A. A., Johnson, H. L., Iriarte, B., Mitchell, R. I., Hallam, K. L., & Sharpless, S., 1961, Publ. U.S. Naval Obs. Second Serie, 17, 343. Li, C. S., 2009, The photometry of three variable stars with Short Period: CY Aqr, GP And, and BP Peg, NTNU, Taipei. McCusky, S. W., & Houk, N., 1964, Astron. J., 69, 412. Pandey, A. K., Upadhyay, K., Ogura, K., Sagar, R., Mohan, V., Mito, H., Bhatt, H. C., & Bhatt, B. C., 2005, MNRS, 358, 1290. Pietrzynski, G.,1996, Acta Astronomica, 46, 357. Pietrzynski, G., 1997, Acta Astronomica, 47, 211. Pigulski, A., Kopacki, G., & Kolaczkowski, Z., 2001, Acta Astronomica, 51, 159. Pigulski, A., Kopacki, G., & Kolaczkowski, Z., 2001, A&A, 376, 144. Phelps, R. L., & Janes, K. A.,. 1991, Mem. S.A.It., 62, 921. Tapia, M., Costero, R., Echevarria, J., & Roth, M., 1991, MNRAS, 253, 649. van den Bergh, S., & de Roux, J., 1978, Astron. J., 83, 1075. WEBDA database, http://www.univie.ac.at/webda/ Wu, C. K., 2004, The Photometry, Kinematics and Dynamics of Two Young Open Clusters: NGC 6910 and Berkeley 87, NTNU, Taipei.. 34.

(42) Appendix 1 Coordinate Transformation The coordinates of stars are not the same in any two frames, because the central target shifts during observing. In order to make the coordinate of a star almost equal in all frames, coordinate transformation must be done. One best frame was taken for reference; coordinates of stars were transformed to best frame by regression. The transformation equations are given as follows:. x   ax  by  c y   dx  ey  f x  , y are transformed coordinates; a, b, c, d, e, f, are coordinate transformation. constants. The constants, a, b, c, d, e, f, and the standard error, a, be, ad, be, for each frame in Region 1 and Region 2 are listed as follows:. In Region 1 frame. a. b. c. a. be. d. e. f. ad. be. 1 2 3 4 5 7 8 9 10 11 12 13 14 15 16 17 18 19 20. 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1. -0.00066 -0.00064 -0.00069 -0.00063 -0.0006 -0.00067 -0.0006 -0.0006 -0.00064 -0.00057 -0.00064 -0.00067 -0.00068 -0.00062 -0.00063 -0.00062 0 -0.00065 -0.00055. 0.0564 0.0472 0.2746 -0.1796 -0.2691 0.3907 -0.7166 -0.4424 -0.4113 -0.1096 0.0154 0.1279 0.0231 0.3908 0.6356 0.8563 0 0.3906 0.1617. 0.000546 0.00055 0.000574 0.000562 0.000563 0.000564 0.000559 0.000568 0.000558 0.000565 0.000555 0.000557 0.000552 0.000553 0.000554 0.000574 0 0.000575 0.000566. 0.000648 0.000653 0.000682 0.000667 0.000668 0.000669 0.000663 0.000674 0.000662 0.000671 0.000658 0.000661 0.000655 0.000656 0.000657 0.000682 0 0.000683 0.000672. 0.0000139 0.0000211 -0.0000185 0.0000002 0.0000742 -0.0000214 -0.0000314 0.0000411 -0.0000094 -0.0000086 0.0000137 -0.0000113 -0.0000252 0.0000307 0.0000474 0.0000487 0 0.0000085 0.0000639. 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1. 0.802 0.895 0.762 0.882 0.597 0.885 0.068 -0.439 0.151 0.276 0.329 0.137 0.285 -0.352 -0.223 -0.333 0 -0.12 -0.03. 0.0000391 0.000007 0.000041 0.0000374 0.0000339 0.0000145 0.0000566 0.0000281 0.000025 0.0000532 0.0000342 0.0000439 0.0000252 0.0000152 0.0000269 0.0000156 0 0.0000183 0.0000397. 0.0000464 0.0000084 0.0000487 0.0000444 0.0000402 0.0000172 0.0000672 0.0000333 0.0000297 0.0000631 0.0000405 0.0000521 0.0000299 0.0000181 0.0000319 0.0000186 0 0.0000217 0.0000471. 35.

(43) 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 58 59. 1 1 1 1 1 1 1 1 1 1 1 0.999 1 0.999 1 0.999 0.999 1 0.999 0.999 0.999 0.999 0.999 1 0.999 0.999 0.999 1 1 0.999 0.999 0.999 0.999 0.999 1 0.999 1 0.999. -0.00064 -0.00068 -0.00059 -0.00068 -0.0007 -0.00065 -0.00065 -0.00046 -0.0007 -0.00067 -0.00068 0.000039 -0.00066 -0.0007 -0.00071 -0.00068 -0.00075 -0.00065 -0.0013 -0.00067 -0.00065 -0.00062 -0.0007 -0.00067 -0.00065 -0.00069 -0.00074 -0.0007 -0.00075 -0.00073 -0.0007 -0.00065 -0.00067 -0.00073 -0.00067 -0.00075 -0.00077 -0.00077. 0.7758 1.6152 0.7603 1.97 1.8994 1.6683 1.5792 1.5381 2.1085 1.8107 2.1995 1.921 1.9451 2.2993 2.2432 2.2982 2.2883 2.2253 2.5665 2.5169 1.9393 1.9291 3.4284 3.3713 2.5947 2.8021 3.277 2.9429 3.2006 3.382 3.8409 3.5252 3.4136 3.9093 4.1606 3.5452 5.3721 4.6876. 0.000572 0.000559 0.000576 0.000545 0.000569 0.000563 0.000563 0.000586 0.000569 0.000569 0.000557 0.000861 0.000567 0.000561 0.000553 0.000572 0.000578 0.000575 0.001125 0.000553 0.000567 0.000553 0.00054 0.00056 0.000566 0.000558 0.000561 0.000535 0.00056 0.000554 0.000567 0.000572 0.000565 0.000563 0.00055 0.000591 0.000555 0.000548. 0.000679 0.000663 0.000684 0.000647 0.000675 0.000668 0.000669 0.000696 0.000676 0.000675 0.000661 0.001022 0.000673 0.000666 0.000657 0.000679 0.000686 0.000683 0.001336 0.000656 0.000674 0.000656 0.000641 0.000665 0.000671 0.000663 0.000665 0.000635 0.000664 0.000657 0.000673 0.000679 0.00067 0.000669 0.000652 0.000702 0.000659 0.00065. 36. 0.0000483 0.0000107 0.0000601 -0.0000255 -0.0000364 0.0000398 0.0000419 0.0000585 -0.00002 -0.0000479 -0.0000065 0.0000109 0.0000342 -0.0000145 0.0000006 0.0000517 -0.0000023 -0.0000264 0.0000602 0.0000133 0.0000376 0.0000475 -0.000018 0.000005 0.0000238 0.0000235 -0.0000771 0.000001 0.0000042 0.0000286 -0.0000221 0.000021 0.0000123 -0.0000169 0.0000861 -0.0000043 -0.0002185 -0.0000585. 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1. -0.153 -0.245 -0.148 0.013 0.027 -0.294 -0.428 -0.551 -0.644 -0.846 -0.849 -0.832 -1.196 -1.187 -1.616 -2.127 -2.195 -2.412 -2.294 -2.117 -2.055 -2.728 -2.77 -2.969 -3.115 -3.231 -3.655 -4.121 -4.313 -4.259 -4.441 -4.706 -4.883 -4.792 -5.119 -5.235 -6.973 -7.163. 0.0000239 0.0000216 0.0000278 0.0000482 0.0000211 0.0000359 0.0000361 0.0000414 0.00001 0.0000347 0.0000262 0.0000212 0.000034 0.0000156 0.0000269 0.0000328 0.00003 0.0000146 0.0000414 0.0000314 0.0000231 0.0000482 0.0000327 0.0000141 0.0000284 0.0000369 0.000012 0.0000423 0.0000269 0.0000326 0.0000575 0.0000165 0.0000269 0.0000456 0.0000199 0.0000286 0.0001168 0.0000331. 0.0000283 0.0000257 0.000033 0.0000572 0.0000251 0.0000426 0.0000428 0.0000492 0.0000119 0.0000412 0.0000311 0.0000252 0.0000403 0.0000185 0.0000319 0.0000389 0.0000356 0.0000173 0.0000491 0.0000373 0.0000275 0.0000572 0.0000388 0.0000168 0.0000338 0.0000438 0.0000142 0.0000502 0.0000319 0.0000386 0.0000682 0.0000195 0.000032 0.0000541 0.0000236 0.000034 0.0001386 0.0000393.

(44) In Region 2 frame. a. b. c. a. be. d. e. f. ad. be. 1 2 3 4 5 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45. 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0.999 1 0.999 1 0.999 0.999 1 0.999 0.999 0.999 0.999 0.999 1 0.999. -0.00066 -0.00064 -0.00069 -0.00063 -0.0006 -0.00067 -0.0006 -0.0006 -0.00064 -0.00057 -0.00064 -0.00067 -0.00068 -0.00062 -0.00063 -0.00062 0 -0.00065 -0.00055 -0.00064 -0.00068 -0.00059 -0.00068 -0.0007 -0.00065 -0.00065 -0.00046 -0.0007 -0.00067 -0.00068 0.000039 -0.00066 -0.0007 -0.00071 -0.00068 -0.00075 -0.00065 -0.0013 -0.00067 -0.00065 -0.00062 -0.0007 -0.00067 -0.00065. 0.0564 0.0472 0.2746 -0.1796 -0.2691 0.3907 -0.7166 -0.4424 -0.4113 -0.1096 0.0154 0.1279 0.0231 0.3908 0.6356 0.8563 0 0.3906 0.1617 0.7758 1.6152 0.7603 1.97 1.8994 1.6683 1.5792 1.5381 2.1085 1.8107 2.1995 1.921 1.9451 2.2993 2.2432 2.2982 2.2883 2.2253 2.5665 2.5169 1.9393 1.9291 3.4284 3.3713 2.5947. 0.000546 0.00055 0.000574 0.000562 0.000563 0.000564 0.000559 0.000568 0.000558 0.000565 0.000555 0.000557 0.000552 0.000553 0.000554 0.000574 0 0.000575 0.000566 0.000572 0.000559 0.000576 0.000545 0.000569 0.000563 0.000563 0.000586 0.000569 0.000569 0.000557 0.000861 0.000567 0.000561 0.000553 0.000572 0.000578 0.000575 0.001125 0.000553 0.000567 0.000553 0.00054 0.00056 0.000566. 0.000648 0.000653 0.000682 0.000667 0.000668 0.000669 0.000663 0.000674 0.000662 0.000671 0.000658 0.000661 0.000655 0.000656 0.000657 0.000682 0 0.000683 0.000672 0.000679 0.000663 0.000684 0.000647 0.000675 0.000668 0.000669 0.000696 0.000676 0.000675 0.000661 0.001022 0.000673 0.000666 0.000657 0.000679 0.000686 0.000683 0.001336 0.000656 0.000674 0.000656 0.000641 0.000665 0.000671. 0.0000139 0.0000211 -0.0000185 0.0000002 0.0000742 -0.0000214 -0.0000314 0.0000411 -0.0000094 -0.0000086 0.0000137 -0.0000113 -0.0000252 0.0000307 0.0000474 0.0000487 0 0.0000085 0.0000639 0.0000483 0.0000107 0.0000601 -0.0000255 -0.0000364 0.0000398 0.0000419 0.0000585 -0.00002 -0.0000479 -0.0000065 0.0000109 0.0000342 -0.0000145 0.0000006 0.0000517 -0.0000023 -0.0000264 0.0000602 0.0000133 0.0000376 0.0000475 -0.000018 0.000005 0.0000238. 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1. 0.802 0.895 0.762 0.882 0.597 0.885 0.068 -0.439 0.151 0.276 0.329 0.137 0.285 -0.352 -0.223 -0.333 0 -0.12 -0.03 -0.153 -0.245 -0.148 0.013 0.027 -0.294 -0.428 -0.551 -0.644 -0.846 -0.849 -0.832 -1.196 -1.187 -1.616 -2.127 -2.195 -2.412 -2.294 -2.117 -2.055 -2.728 -2.77 -2.969 -3.115. 0.0000391 0.000007 0.000041 0.0000374 0.0000339 0.0000145 0.0000566 0.0000281 0.000025 0.0000532 0.0000342 0.0000439 0.0000252 0.0000152 0.0000269 0.0000156 0 0.0000183 0.0000397 0.0000239 0.0000216 0.0000278 0.0000482 0.0000211 0.0000359 0.0000361 0.0000414 0.00001 0.0000347 0.0000262 0.0000212 0.000034 0.0000156 0.0000269 0.0000328 0.00003 0.0000146 0.0000414 0.0000314 0.0000231 0.0000482 0.0000327 0.0000141 0.0000284. 0.0000464 0.0000084 0.0000487 0.0000444 0.0000402 0.0000172 0.0000672 0.0000333 0.0000297 0.0000631 0.0000405 0.0000521 0.0000299 0.0000181 0.0000319 0.0000186 0 0.0000217 0.0000471 0.0000283 0.0000257 0.000033 0.0000572 0.0000251 0.0000426 0.0000428 0.0000492 0.0000119 0.0000412 0.0000311 0.0000252 0.0000403 0.0000185 0.0000319 0.0000389 0.0000356 0.0000173 0.0000491 0.0000373 0.0000275 0.0000572 0.0000388 0.0000168 0.0000338. 37.

(45) 46 47 48 49 50 51 52 53 54 55 56 58 59. 0.999 0.999 1 1 0.999 0.999 0.999 0.999 0.999 1 0.999 1 0.999. -0.00069 -0.00074 -0.0007 -0.00075 -0.00073 -0.0007 -0.00065 -0.00067 -0.00073 -0.00067 -0.00075 -0.00077 -0.00077. 2.8021 3.277 2.9429 3.2006 3.382 3.8409 3.5252 3.4136 3.9093 4.1606 3.5452 5.3721 4.6876. 0.000558 0.000561 0.000535 0.00056 0.000554 0.000567 0.000572 0.000565 0.000563 0.00055 0.000591 0.000555 0.000548. 0.000663 0.000665 0.000635 0.000664 0.000657 0.000673 0.000679 0.00067 0.000669 0.000652 0.000702 0.000659 0.00065. 38. 0.0000235 -0.0000771 0.000001 0.0000042 0.0000286 -0.0000221 0.000021 0.0000123 -0.0000169 0.0000861 -0.0000043 -0.0002185 -0.0000585. 1 1 1 1 1 1 1 1 1 1 1 1 1. -3.231 -3.655 -4.121 -4.313 -4.259 -4.441 -4.706 -4.883 -4.792 -5.119 -5.235 -6.973 -7.163. 0.0000369 0.000012 0.0000423 0.0000269 0.0000326 0.0000575 0.0000165 0.0000269 0.0000456 0.0000199 0.0000286 0.0001168 0.0000331. 0.0000438 0.0000142 0.0000502 0.0000319 0.0000386 0.0000682 0.0000195 0.000032 0.0000541 0.0000236 0.000034 0.0001386 0.0000393.

(46) Appendix 2 Plots of magnitude calibration Region 1. 39.

(47) 40.

(48) 41.

(49) 42.

(50) 43.

(51) Region 2. 44.

(52) 45.

(53) 46.

(54) 47.

(55) 48.

(56) 49.

(57) Appendix 3 The data of stars from observation Region 1 No.. X(Pixel). Y(Pixel). 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64. 100.114 100.511 102.867 103.097 103.14 106.281 113.246 113.801 116.814 117.93 118.459 118.879 120.467 121.881 122.553 122.701 123.351 127.757 128.218 128.921 129.087 130.41 130.823 132.372 133.173 136.104 136.224 136.341 136.627 141.23 141.645 142.073 144.301 145.722 145.836 145.98 149.199 150.623 151.302 153.036 153.68 154.147 154.626 156.262 158.578 159.848 160.605 163.388 163.792 164.133 166.546 167.025 167.211 167.345 170.313 170.774 174.117 175.187 175.432 179.453 179.652 182.046 186.58 188.618. 731.822 1058.541 453.097 390.585 658.239 493.685 1054.379 878.817 980.737 466.771 327.47 677.53 966.574 1188.039 446.631 123.256 575.95 612.987 448.82 224.401 527.16 999.472 1075.729 953.103 1054.367 937.917 1115.538 364.432 802.754 121.233 1018.888 1111.868 381.714 1150.827 437.147 143.666 814.036 269.632 384.428 659.052 534.48 614.095 774.08 136.53 481.748 473.306 1183.778 327.2 803.677 876.763 544.338 917.899 973.925 269.136 1097.565 346.038 828.054 708.757 494.315 148.892 275.666 515.443 994.022 754.016. Mag.(V) note No. X(Pixel) Y(Pixel) Mag.(V) note No. X(Pixel) Y(Pixel) Mag.(V) note No. X(Pixel) Y(Pixel) Mag.(V) note 16.14 17.21 17.85 19.32 19.66 17.8 19.38 19.04 18.46 18.81 17.38 14.91 19.56 15.71 19.17 18.93 19.38 16.66 18.97 16.74 17.86 19.74 13.17 18.72 17.16 18.85 18.41 17.81 17.77 14.13 17.27 15.84 15.72 16.23 15.14 16.17 18.01 17.54 16.1 14.23 19.62 18.34 17.82 19.44 17.44 16.49 12.53 18.88 19.39 14.27 17.25 14.79 18.66 19.3 19.47 15.91 16.19 19.96 18.26 19.04 19.52 18.99 13.19 19.16. 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128. 191.408 192.043 193.581 195.046 195.564 197.343 200.326 207.775 209.094 213.752 216.279 217.196 220.434 222.047 223.533 223.739 225.79 226.374 228.674 229.449 229.801 231.483 232.11 232.277 234.593 239.323 241.214 241.431 242.655 243.685 244.298 245.315 245.509 246.494 249.618 250.092 250.645 250.759 250.88 253.708 255.014 256.857 257.054 258.393 260.073 262.408 263.115 269.763 270.917 271.41 277.685 277.727 277.769 281.037 281.162 281.588 282.716 285.477 285.724 288.814 289.477 292.065 292.739 293.143. 511.459 606.861 166.595 356.209 1163.428 351.977 885.655 902.828 1124.289 214.555 717.464 1112.187 265.011 303.407 892.445 278.487 747.305 1011.093 572.424 293.305 128.711 210.256 577.265 551.914 848.755 1133.544 685.343 221.797 189.285 784.544 834.193 993.745 858.449 791.705 326.532 883.562 1180.817 912.775 430.155 437.131 231.971 271.207 1139.602 844.845 123.192 1098.833 1179.233 919.651 1090.536 254.66 614.973 1060.291 818.109 254.159 842.895 498.423 132.442 347.34 477.464 592.966 547.109 654.99 390.741 1134.886. 18.15 19.74 18.6 15.81 18.67 18.74 17.68 17.26 17.73 20.08 19.17 15.16 15.99 19.62 18.34 19.6 15.75 17.95 17.13 13.89 18.64 16.49 17.55 15.17 16.57 17.94 19.56 15.4 19.44 17.43 18.12 16.86 13.93 19.37 15.62 16.86 15.95 17.81 18.71 17.32 17.48 19.06 19.25 16.99 19.27 19.1 17.23 15.34 18.2 16.17 18.43 15.26 14.18 19.14 15.54 17.97 13.33 19.73 16.66 19.73 17.6 16.17 18.62 17.58. 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192. 50. 297.021 297.916 298.246 298.645 298.647 300.613 300.632 301.767 302.026 302.604 304.064 308.584 309.395 311.656 313.397 313.891 313.915 314.506 315.143 316.279 316.462 317.577 317.706 319.247 323.065 323.111 323.884 324.422 325.208 327.34 328.619 328.627 329.205 331.041 331.243 331.511 331.579 331.77 336.569 336.577 337.228 340.611 342.751 342.979 345.963 346.609 353.997 356.066 356.52 358.443 361.414 362.202 362.854 363.739 367.688 370.616 371.107 374.056 374.426 374.511 376.214 377.399 378.523 380.737. 744.334 89.425 521.027 102.72 842.957 1110.569 679.751 155.28 392.339 643.42 258.591 245.066 748.259 693.625 1044.584 609.746 1104.42 228.947 986.865 752.09 926.031 603.03 865.581 1158.125 902.079 820.393 466.515 1001.247 399.762 876.475 728.169 752.348 649.361 626.684 308.923 1059.677 805.236 874.013 249.847 904.845 726.593 154.112 747.269 602.803 922.496 462.607 573.596 968.777 807.699 409.535 688.144 418.913 718.005 904.383 182.192 928.4 845.22 1097.828 309.975 917.202 564.739 1043.027 905.818 772.259. 18.35 17.69 17.47 19.31 16.06 16.58 18.52 17.53 18.99 18.25 16.7 19.46 19.56 17.68 19.78 17.89 14.36 16.77 17.33 17.49 13.9 19.99 18.23 16.55 19.89 19.15 19 19.71 14.94 19 19.22 16.76 20.02 15.49 18.99 17.09 15.3 17.6 15.73 15.08 17.88 15.58 17.45 18.47 18.61 15.64 18.37 17.11 18.34 19.11 16.93 19.72 16.14 18.56 17.51 14.22 19.92 17.55 17.62 18.59 18.06 13.92 17.82 18.18. 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256. 381.049 382.719 384.865 385.408 386.571 387.969 390.564 394.409 397.122 397.296 397.917 399.98 400.521 403.803 405.511 413.564 415.002 415.707 416.398 416.432 416.781 417.465 418.697 419.291 420.501 420.831 421.99 422.969 423.519 425.747 427.253 427.643 427.802 428.089 429.455 429.505 429.843 431.871 432.293 436.992 437.095 438.032 438.342 439.27 441.222 442.248 445.116 445.786 446.945 449.348 449.349 450.194 450.826 451.241 451.439 452.382 452.437 457.821 458.07 458.221 461.945 462.055 462.733 466.153. 556.625 1139.605 157.495 764.531 192.685 769.961 505.231 1115.274 726.267 467.835 694.876 903.315 859.023 1125.927 602.446 1149.662 1073.808 1067.753 758.856 236.817 944.978 849.207 567.131 265.918 1192.819 864.398 826.272 359.745 439.241 768.469 664.488 652.497 1182.117 120.122 546.645 465.21 616.523 785.17 1061.372 970.959 684.594 197.593 1115.479 853.445 98.554 498.789 1102.748 1021.588 902.471 319.531 1022.991 724.614 507.089 588.207 159.813 569.293 1104.998 541.352 696.996 679.696 558.513 1010.057 644.505 484.961. 16.93 19.39 16.22 19.15 18.72 19.28 18.23 16.49 19.28 16.44 18.72 19.84 17.48 19.11 17.38 19.87 19.1 17.08 20.1 16.62 15.65 17.06 14.28 18.94 18.91 15.69 20.07 19.04 19.03 18.46 17.41 15.23 17.46 19.46 15.44 18.56 15.58 19.61 18.65 18.48 15.96 12.57 17.35 16.69 19.03 17.13 13.97 19.42 17.06 19 18.51 18.45 19.92 16.11 19.34 17.63 19.3 18.57 19.52 18.41 19.28 16 14.62 17.86.

(58) No.. X(Pixel). Y(Pixel). 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326. 466.418 467.533 467.625 467.638 470.379 472.763 473.253 477.329 479.293 482.14 482.325 483.28 485.942 487.359 488.014 489.2 490.432 491.227 491.635 492.038 493.351 493.623 496.121 498.519 498.887 502.694 504.584 505.657 507.623 507.887 509.294 510.287 511.145 513.89 515.788 516.162 518.172 520.203 520.335 521.375 521.601 525.743 526.931 527.437 528.788 529.05 529.476 529.625 532.889 534.12 536.861 537.745 538.361 546.403 551.384 551.911 554.064 554.525 556.026 560.543 562.699 563.731 564.193 564.485 564.567 564.669 565.091 565.11 565.281 567.72. 1085.047 514.105 574.716 149.575 648.973 1066.701 1154.103 267.565 767.806 787.259 642.821 1178.203 447.641 878.617 481.492 707.736 639.027 679.487 776.854 967.897 725.872 1131.505 1063.196 1076.147 744.189 1012.284 409.288 467.047 259.365 340.026 366.949 951.959 797.805 880.017 766.182 233.923 193.274 632.506 1108.425 930.343 754.885 993.689 347.498 998.065 789.224 523.148 1060.77 304.049 1103.079 231.18 611.735 285.175 298.125 1071.963 717.507 934.434 895.461 837.851 415.337 406.11 1106.875 514.971 617.318 559.092 1189.236 177.487 400.547 380.935 1036.483 77.78. Mag.(V) note No. X(Pixel) Y(Pixel) Mag.(V) note No. X(Pixel) Y(Pixel) Mag.(V) note No. X(Pixel) Y(Pixel) Mag.(V) note 19.11 18.33 17.13 19.67 19.52 17.43 19.91 19.35 18.16 19.49 19.15 17.99 14.38 15.56 17.54 17.43 19.18 19.65 12.68 10.83 14.6 15.25 19.81 19.35 16.1 19.02 16.75 18.87 16.44 12.37 18.79 18.8 17.62 18.86 19.06 19.15 16.53 18.3 18.71 13.38 15.53 17.63 17.76 15.11 17.83 15.59 15.96 19.61 18.77 19.64 14.08 19.36 19.4 17.85 17.94 15.47 19.08 18.37 17.19 18.41 18.15 19.51 16.37 19.52 19.73 15.6 17.46 19.26 17.33 16.4. 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396. 573.612 574.258 575.354 576.628 578.473 579.347 580.572 582.323 582.53 582.829 585.558 585.713 587.632 588.346 589.022 589.076 589.772 593.977 594.387 595.892 597.624 599.789 600.219 601.308 602.582 603.601 604.985 605.958 606.089 606.197 606.254 606.781 607.786 608.693 609.02 609.55 611.318 611.664 613.019 613.61 613.69 615.043 615.261 615.285 616.475 617.545 618.64 618.678 619.134 619.257 619.577 620.177 621.843 623.145 624.472 624.84 626.684 627.826 629.072 631.288 632.495 632.995 634.986 635.173 635.625 637.593 639.133 641.2 642.057 643.102. 912.692 519.019 229.849 978.919 873.779 628.157 512.909 110.376 746.551 684.791 1116.819 1124.599 588.614 1078.919 538.528 1028.337 460.482 967.492 725.473 792.085 988.445 180.104 1161.43 499.294 176.298 709.442 574.236 899.532 1124.641 628.26 753.945 952.039 1000.151 410.64 175.647 800.987 564.758 768.754 1069.484 861.767 460.964 790.91 1176.005 103.364 633.879 418.55 1016.032 808.055 197.433 1128.822 962.208 1044.957 618.604 721.176 1027.575 186.855 321.086 116.531 516.32 984.463 1144.55 335.684 916.363 1096.135 455.178 745.038 532.832 665.746 563.941 1001.92. 19.83 16.53 17.95 17.24 16.54 17.22 17.11 19.13 16.44 17.08 17.87 18.15 19.63 16.62 20.22 16.17 20.41 18.61 12.79 19.51 19.63 19 18.78 17.92 17.14 16.43 19.11 15.83 19.1 14.94 20.03 18.42 18.96 19.97 17.86 20.5 16.17 19.67 19.49 19.47 18.2 19.73 17.96 16.7 18.13 15.91 18.92 19.15 15.75 19.24 14.76 15.27 17.83 15.09 18.02 18.16 18.9 18.47 15.74 14.05 17.38 17.41 18.02 18.38 19.26 19.08 18.17 12.82 16.58 19.33. 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466. 51. 645.051 645.224 645.292 647.575 648.118 649.679 652.877 655.53 655.945 658.494 660.265 661.167 661.386 662.002 662.039 663.407 664.178 665.195 665.473 667.352 668.319 670.437 672.426 672.662 672.778 673.586 673.807 674.242 676.09 676.322 680.954 682.244 683.226 685.193 685.277 686.145 688.05 688.665 689.331 689.563 690.061 690.196 690.414 692.703 693.678 694.328 697.478 701.827 702.135 702.91 704.697 705.335 705.692 707.635 707.716 709.161 709.565 712.982 713.602 713.923 715.009 715.056 715.312 715.415 717.669 719.01 719.023 719.259 719.623 720.115. 760.761 222.672 899.113 890.168 1028.071 776.808 263.371 228.23 987.033 1128.188 561.099 1035.198 641.879 869.314 1137.941 476.419 417.431 225.474 135.51 284.162 933.841 1199.313 1073.447 997.883 648.527 833.533 1125.199 658.888 277.294 538.869 547.73 487.033 1042.407 505.105 658.109 1113.495 544.353 804.675 708.662 887.058 646.86 370.744 165.568 422.192 1119.857 1108.414 129.041 470.612 404.647 360.509 356.369 689.359 92.784 920.818 708.906 598.232 145.2 706.322 213.449 854.201 317.303 1003.705 861.03 1185.464 845.618 719.568 601.739 1194.731 314.639 1036.138. 20.1 17.82 17.26 17.98 18.41 18.52 15.85 18.69 19.81 16 18.35 19.28 19.63 19.21 20.01 20.12 18.35 18.84 19.76 15.41 19.93 20.05 18.37 16.73 18.83 15.46 16.85 15.19 19.02 11.82 14.64 16.84 12.51 18.56 14.35 14.01 18.07 16.5 19.63 19.26 19.19 20.07 18.95 19.13 19.72 18.81 12.35 19.15 18.99 18.34 18.93 18.04 18.78 19.39 14.17 14.5 19.61 13.86 20.19 16.84 20 12.05 20.08 13.52 18.56 17.07 18.33 18.74 19.76 14.95. 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 ※ 534 535 536. 721.685 724.573 724.754 724.766 725.005 725.045 725.228 728.716 730.652 730.823 730.892 731.224 732.633 733.602 734.097 734.101 735.528 737.168 738.942 739.064 744.298 745.983 746.527 747.013 747.865 748.775 750.087 751.863 752.856 755.56 758.457 759.353 761.455 765.149 765.204 766.189 766.303 766.761 767.32 768.126 771.495 771.552 773.843 777.366 777.548 778.325 779.193 782.184 784.498 785.614 786.339 788.825 789.096 789.884 793.723 795.001 795.136 798.602 801.29 801.518 801.869 801.882 803.547 803.548 803.794 804.076 804.782 806.582 806.959 808.824. 482.789 1000.866 584.3 838.193 91.836 544.253 553.331 629.699 250.061 86.582 977.061 912.835 1102.639 525.217 172.499 584.804 433.203 1125.019 813.827 732.432 144.311 837.132 128.274 814.797 524.399 845.991 407.154 178.504 925.477 114.788 327.87 1070.452 878.071 132.654 859.996 906.344 435.453 1013.213 1111.424 293.547 1045.68 128.826 614.309 718.672 691.387 1170.158 442.323 861.071 1096.14 626.734 1152.066 881.18 146.326 826.59 206.164 1151.354 1115.18 748.635 133.953 529.792 100.705 367.721 479.389 807.333 347.583 118.765 507.848 889.039 510.202 1103.273. 18.02 15.77 17.65 18 19.14 20.21 18.07 15.4 17.56 19.31 16.46 19.43 17.35 18.18 17.91 16.36 14.2 15.21 19.68 18.34 18.89 19.32 19.12 16.84 14.82 17.57 18.03 17.74 18.23 16.92 18.94 19.63 16.21 17.69 18.96 18.43 16.81 18.73 17.83 18.88 18.73 15.85 15.13 19.19 19.48 17.17 18.88 11.07 15.59 13.85 15.45 16.9 19.57 17.76 15.2 15.53 19.94 18.93 18.39 18.55 18.22 17.56 17.69 16.87 18.78 18.23 19.13 18.28 18.79 16.55. ※.

(59) No.. X(Pixel). Y(Pixel). 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606. 810.607 810.748 810.783 811.715 814.139 814.701 814.859 814.967 815.577 817.033 817.312 819.795 820.428 820.668 821.856 822.783 823.571 825.891 826.644 827.683 828.254 829.968 830.055 832.108 832.386 833.649 834.086 835.208 835.892 836.892 837.599 838.017 840.22 840.83 841.917 843.275 844.037 845.601 846.761 846.844 847.17 848.129 848.247 849.517 850.825 850.905 851.006 851.873 852.712 854.776 855.813 858.743 859.176 860.727 863.3 864.412 864.748 865.714 865.766 866.842 867.089 868.264 869.081 869.247 870.496 873.508 874.09 874.716 874.926 876.344. 398.429 770.978 274.938 1110.506 779.068 1088.721 1115.749 429.907 336.306 820.473 1192.651 487.207 939.86 1131.749 1189.786 326.51 765.028 398.158 60.16 684.55 905.384 236.225 611.299 1107.679 227.454 536.874 1062.161 708.837 826.77 945.686 222.562 750.264 922.823 1130.421 394.093 814.37 1004.546 1041.51 654.014 963.216 1107.677 1010.425 744.64 1172.177 1135.189 372.486 775.182 94.861 594.732 199.111 1098.421 683.125 1163.082 775.241 1062.908 443.981 296.997 913.277 767.621 640.69 820.771 497.625 966.367 571.333 347.29 1035.248 266.84 1158.872 778.843 102.243. Mag.(V) note No. X(Pixel) Y(Pixel) Mag.(V) note No. X(Pixel) Y(Pixel) Mag.(V) note No. X(Pixel) Y(Pixel) Mag.(V) note 12.95 13.02 16.94 19.52 16.1 18.79 19.24 17.56 19.58 17.88 17.62 18.41 18.61 16.45 17.58 18.91 11.08 19.63 14.18 17.27 15.54 19.82 17.23 13.78 16.8 17.97 11.57 16.65 20.26 16.27 14.31 15.94 14.94 16.14 18.79 18.92 14.18 15.04 19.73 13.55 18.25 19.81 14.27 12.94 16.02 19.71 15.86 16.49 19.66 16.5 19.17 19.24 14.13 18.92 15.85 16.6 17.88 19.97 18.06 14.84 12.27 16.94 13.36 16.71 14.06 18.95 19.67 15.08 19.32 19.61. 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676. 876.887 877.488 878.58 880.079 882.421 883.388 883.738 885.085 885.289 885.725 886.258 886.291 886.325 886.942 887.425 887.843 888.776 888.918 889.094 889.323 891.482 892.621 894.413 895.434 896.008 897.711 898.769 900.092 901.015 901.262 902.02 902.401 902.51 902.851 902.867 904.068 904.301 904.42 906.274 907.833 909.172 910.369 912.474 912.903 913.626 920.654 921.047 924.168 924.25 924.677 924.944 926.613 928.43 929.536 930.171 930.23 930.342 931.322 931.624 931.883 935.178 936.1 936.462 938.308 938.423 942.276 943.112 943.705 943.796 945.206. 1151.706 862.124 313.413 1158.734 1010.254 322.843 621.166 923.192 806.924 552.359 573.47 889.983 871.006 569.816 233.075 1180.239 466.386 70.022 1030.779 1090.513 832.412 960.482 1117.265 355.652 870.142 910.845 315.578 578.061 90.647 1074.498 549.112 1104.27 1198.789 74.606 895.958 329.297 918.778 979.475 385.255 551.897 1067.67 946.295 836.836 983.95 451.338 952.279 457.445 1191.18 292.085 140.068 297.729 476.421 1158.024 920.544 662.92 935.832 170.038 855.248 803.165 1047.143 408.601 1013.028 902.63 191.002 954.941 1059.096 563.137 189.731 728.799 1156.818. 18.41 19.08 14.99 17 18.63 15.09 14.49 13.53 19.08 18.15 11.26 18.49 20.4 11.48 16.88 17.84 19.86 19.32 15.97 15.58 14.68 19.74 16.03 14.47 16.37 16.1 19.95 10.74 20.02 17.46 19.37 18.65 20.62 19.65 19.83 18.64 18.37 15.24 18.93 15.32 19.72 18.15 15.77 20.27 19.33 18.79 13.02 12.67 19.69 19.16 19.37 15.09 19.04 18.24 18.9 14.51 18.2 17.91 15.8 18.98 17.34 13.29 12.18 20.01 18.98 20.02 17.93 18.73 12.22 19.08. 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746. 52. 946.342 946.41 948.389 948.916 949.516 950.576 951.774 952.919 953.038 953.247 955.273 956.216 956.763 957.414 957.544 958.58 959.134 960.119 960.614 963.299 963.555 963.562 963.798 964.801 965.042 966.133 966.4 966.723 967.178 967.518 967.963 969.79 970.981 971.388 972.555 972.749 973.616 973.778 977.104 977.281 978.362 979.648 979.766 981.845 981.919 984.414 984.53 984.817 986.488 987.383 988.317 989.213 990.573 990.665 991.365 991.542 992.557 992.71 993.098 993.311 994.926 995.173 997.06 997.143 997.416 997.585 997.666 997.734 998.064 999.047. 494.318 673.722 872.892 788.008 707.712 1166.043 1023.581 806.596 712.071 558.989 383.689 1097.333 862.752 884.726 747.479 665.857 849.807 1152.505 1089.326 708.711 1137.221 915.873 661.302 454.711 1164.32 1103.292 806.041 860.892 907.88 971.619 958.761 910.351 692.451 598.775 739.788 1111.151 938.247 425.493 502.229 832.822 100.079 234.879 941.118 729.699 529.437 461.868 973.763 1185.932 102.254 229.867 820.066 758.707 1111.282 177.374 788.929 256.408 978.095 270.758 1079.225 767.58 714.801 457.315 1111.035 698.802 960.247 837.691 592.937 1184.395 358.046 794.004. 19.99 20.17 17.75 19.13 19.47 19.05 18.49 16.63 19.62 15.62 17.91 19.28 13.84 17.66 15.61 19.39 18.94 19.99 20.09 17.48 18.17 14.9 16.41 19.04 14.77 18.21 12.66 13.36 17.6 10.71 18.94 17.94 16.76 19.88 15.77 18.87 18.74 15.47 18.8 14.02 17.48 17.4 16.85 18.68 14.4 18.58 19.17 21.42 15.84 19.15 16.74 15.36 18.69 19.17 14.96 18.58 16.06 19.46 18.18 12.2 16.81 18.7 19.77 18.81 12.39 19.35 18.82 13.48 17.79 12.75. 747 999.39 748 999.667 749 1003.374 750 1003.671 751 1008.404 752 1009.108 753 1009.739 754 1010.087 755 1014.067 756 1014.34 757 1015.3 758 1015.347 759 1015.939 760 1016.356 761 1016.65 762 1017.271 763 1018.852 764 1019.253 765 1019.686 766 1021.572 767 1021.747 768 1024.563 769 1025.525 770 1026.138 771 1026.675 772 1027.977 773 1028.104 774 1029.491 775 1029.787 ※ 776 1031.377 777 1032.237 778 1032.478 779 1034.139 780 1034.72 781 1035.891 782 1037.329 783 1038.045 784 1038.125 785 1039.03 786 1039.421 787 1039.43 788 1040.503 789 1042.028 790 1042.235 791 1042.387 792 1042.956 793 1043.487 794 1044.217 795 1045.326 796 1045.821 797 1045.998 798 1047.335 799 1047.81 800 1048.017 801 1048.649 802 1048.776 803 1048.924 804 1050.384 805 1050.811 806 1050.969 807 1051.375 808 1051.687 809 1052.454 810 1053.63 811 1053.635 812 1053.755 813 1055.821 814 1056.273 815 1056.645 816 1057.995. 508.745 661.69 564.377 712.54 929.03 481.739 498.066 699.466 752.232 409.776 877.969 296.023 1061.951 982.675 1044.924 526.058 937.308 204.386 761.74 208.183 429.746 442.596 976.104 514.853 880.665 120.972 388.057 788.467 679.466 541.863 1008.196 1192.474 914.67 526.747 478.022 818.391 340.03 1035.762 803.961 200.662 1101.438 677.138 356.734 733.445 578.63 859.377 654.164 327.656 472.646 618.326 72.303 319.566 93.334 625.613 612.137 631.478 378.551 1086.565 1063.013 481.295 618.573 303.817 1096.972 551.084 695.903 496.443 982.779 725.421 858.085 507.173. 19.18 19.85 17.48 12.28 17.27 19 15.59 17.83 17.99 16.52 18.92 14.14 20.3 16.73 18.99 20.19 19.15 19.1 14.51 19.87 14.16 18.99 19.74 19.24 19.4 18.87 19.7 12.81 16.48 18.92 18.39 18.54 13.56 14.67 19.57 18.57 19.61 19.96 19.69 19.06 19.75 19.47 19.9 18.42 19.12 18.18 13.9 16.81 16.11 11.12 19.45 18.07 19.62 11.06 11.68 12.34 20 19.98 17.86 16.84 10.65 18.39 19.21 13.64 14.95 18.7 19.31 17.44 11.57 19.24. ※.