Telescopes In Education (TIE) - Heath Gibson's Report

Analysis of a Newly Identified Variable Star In Aquarius

Heath Gibson

After calculating the magnitude of variable N in each image, I plotted this against the Julian time at which it was exposed, deriving a light curve. Table 6 contains the data used to plot the light curves for variable candidate N in figures 4 and 5.

After graphing the first light curve (Figure 4), I observed a noticeable bulge at the bottom of the minimum in the sinusoidal curve. Upon closer inspection, it appeared that there were two minima graphed into the same minimum‹the first minimum seemed to reach its nadir five hundredths of a magnitude higher than the second. In order to test this theory, I doubled the period of the curve to see if the two minima could be separated from each other (the original period was 0.15315 days; doubled, it became 0.3063 days) in a new curve (Figure 5). Although there were not enough data points to fill in the part of the curve in phase 0.6 to 0.7, the necessary information to make an educated guess on the variable¼s type was present. On the new light curve, there could be seen two distinct minima separated by half a phase; this indicated that the actual period was 0.3063 days. I determined that between the first and second minimum there was a magnitude difference of 0.04, while the magnitude of the variable at each maximum remained constant.

This light curve suggested a contact binary system‹due to its very short period‹with two stars of roughly the same magnitude. With the help of my mentors, I learned that this eclipsing binary (EB) had properties very similar to a W Urase Majoris (W UMa) EB. Using the Caltech library, I found the light curve of a W UMa-type system located in RZ Tauri and found the curve and period to be almost identical to mine. Like my variable, the W UMa had a short period of seven to eight hours; my variable had a period of 0.3063 days, while RZ Tauri had a period of 0.362 days. The light curves were also very similar, as can be observed in Figures 5 and 6. Figure 5, my light curve, has a difference of 0.04 magnitudes between the first and second minima; the W UMa RZ Tauri EB¼s magnitude difference between minima is 0.05. The similarity between these two variables show a considerable possibility that variable N is indeed a W UMa type binary system

Table 6. Table of magnitudes and times for variable star N as graphed in Figure 5

Julian Day	R	Regular	Phase	Phase
2450000+		Phase	Repeat	Repeat
			Add 1	Subtract 1

1475.6504	13.52	0.2551	1.2551	-0.7449
1475.6535	13.47	0.2450	1.2450	-0.7550
1475.6562	13.58	0.2362	1.2362	-0.7638
1475.6593	13.51	0.2261	1.2261	-0.7739
1475.6619	13.53	0.2176	1.2176	-0.7824
1475.6646	13.54	0.2088	1.2088	-0.7912
1475.6672	13.62	0.2003	1.2003	-0.7997
1475.6698	13.55	0.1918	1.1918	-0.8082
1475.6723	13.59	0.1836	1.1836	-0.8164
1475.6748	13.59	0.1755	1.1755	-0.8245
1475.6775	13.61	0.1667	1.1667	-0.8333
1475.6806	13.61	0.1566	1.1566	-0.8435
1475.6832	13.61	0.1481	1.1481	-0.8519
1475.6857	13.69	0.1399	1.1399	-0.8601
1475.6885	13.65	0.1308	1.1308	-0.8693
1475.6910	13.64	0.1226	1.1226	-0.8774
1475.6936	13.53	0.1141	1.1141	-0.8859
1475.6973	13.71	0.1020	1.1020	-0.8980
1475.6998	13.73	0.0939	1.0939	-0.9061
1475.7023	13.78	0.0857	1.0857	-0.9143
1475.7048	13.74	0.0775	1.0775	-0.9225
1475.7075	13.86	0.0687	1.0687	-0.9313
1475.7100	13.89	0.0606	1.0606	-0.9394
1475.7126	13.93	0.0521	1.0521	-0.9479
1475.7151	13.97	0.0439	1.0439	-0.9561
1475.7176	14.03	0.0358	1.0358	-0.9643
1475.7201	14.08	0.0276	1.0276	-0.9724
1475.7230	14.04	0.0181	1.0181	-0.9819
1475.7255	14.07	0.0100	1.0100	-0.9900
1475.7281	14.11	0.0015	1.0015	-0.9985
1475.7356	14.07	-0.0230	0.9770	-1.0230
1475.7382	14.01	-0.0315	0.9685	-1.0315
1475.7407	13.96	-0.0397	0.9603	-1.0397
1475.7433	13.93	-0.0482	0.9518	-1.0482
1475.7458	13.87	-0.0563	0.9437	-1.0563
1475.7511	13.80	-0.0736	0.9264	-1.0736
1475.7536	13.72	-0.0818	0.9182	-1.0818
1475.7585	13.70	-0.0978	0.9022	-1.0978
1475.7686	13.63	-0.1308	0.8693	-1.1308
1475.7711	13.60	-0.1389	0.8611	-1.1389
1475.7736	13.64	-0.1471	0.8529	-1.1471
1475.7763	13.60	-0.1559	0.8441	-1.1559
1475.7788	13.59	-0.1641	0.8360	-1.1641
1475.7813	13.55	-0.1722	0.8278	-1.1722
1475.7841	13.58	-0.1814	0.8186	-1.1814
1475.7865	13.56	-0.1892	0.8108	-1.1892
1475.7890	13.55	-0.1974	0.8026	-1.1974
1475.7918	13.64	-0.2065	0.7935	-1.2065
1475.7943	13.59	-0.2147	0.7853	-1.2147
1475.7969	13.54	-0.2232	0.7769	-1.2232
1475.7993	13.53	-0.2310	0.7690	-1.2310
1475.8018	13.55	-0.2391	0.7609	-1.2391
1475.8043	13.53	-0.2473	0.7527	-1.2473
1476.6259	13.83	0.5704	1.5704	-0.4296
1476.6292	13.84	0.5596	1.5596	-0.4404
1476.6319	13.92	0.5508	1.5508	-0.4492
1476.6346	13.98	0.5420	1.5420	-0.4581
1476.6372	14.02	0.5335	1.5335	-0.4665
1476.6397	14.06	0.5253	1.5253	-0.4747
1476.6427	14.10	0.5155	1.5155	-0.4845
1476.6454	14.11	0.5067	1.5067	-0.4933
1476.6482	14.14	0.4976	1.4976	-0.5025
1476.6508	14.13	0.4891	1.4891	-0.5109
1476.6534	14.10	0.4806	1.4806	-0.5194
1476.6561	14.12	0.4718	1.4718	-0.5282
1476.6586	14.04	0.4636	1.4636	-0.5364
1476.6610	13.99	0.4558	1.4558	-0.5442
1476.6635	13.93	0.4476	1.4476	-0.5524
1476.6661	13.86	0.4391	1.4391	-0.5609
1476.6686	13.88	0.4310	1.4310	-0.5691
1476.6711	13.83	0.4228	1.4228	-0.5772
1476.6736	13.83	0.4146	1.4146	-0.5854
1476.6773	13.76	0.4026	1.4026	-0.5975
1476.6798	13.73	0.3944	1.3944	-0.6056
1476.6823	13.73	0.3862	1.3862	-0.6138
1476.6847	13.69	0.3784	1.3784	-0.6216
1476.6993	13.59	0.3307	1.3307	-0.6693
1476.7018	13.59	0.3226	1.3226	-0.6774
1476.7045	13.59	0.3137	1.3137	-0.6863
1476.7067	13.58	0.3066	1.3066	-0.6934
1476.7095	13.57	0.2974	1.2974	-0.7026
1476.7122	13.57	0.2886	1.2886	-0.7114
1476.7147	13.55	0.2804	1.2804	-0.7196
1476.7172	13.57	0.2723	1.2723	-0.7277
1476.7197	13.53	0.2641	1.2641	-0.7359
1476.7227	13.57	0.2543	1.2543	-0.7457
1476.7254	13.55	0.2455	1.2455	-0.7545
1476.7282	13.55	0.2364	1.2364	-0.7636
1476.7308	13.56	0.2279	1.2279	-0.7721
1476.7333	13.56	0.2197	1.2197	-0.7803
1476.7359	13.55	0.2112	1.2112	-0.7888
1476.7385	13.53	0.2027	1.2027	-0.7973
1476.7411	13.56	0.1943	1.1943	-0.8058
1476.7445	13.56	0.1832	1.1832	-0.8169
1476.7470	13.57	0.1750	1.1750	-0.8250
1476.7495	13.58	0.1668	1.1668	-0.8332
1476.7520	13.58	0.1587	1.1587	-0.8413
1476.7546	13.59	0.1502	1.1502	-0.8498
1476.7573	13.62	0.1414	1.1414	-0.8586
1476.7608	13.63	0.1299	1.1299	-0.8701
1476.7633	13.65	0.1218	1.1218	-0.8782
1476.7658	13.66	0.1136	1.1136	-0.8864
1476.7683	13.68	0.1055	1.1055	-0.8946
1476.7710	13.67	0.0966	1.0966	-0.9034
1476.7739	13.72	0.0872	1.0872	-0.9128
1476.7764	13.76	0.0790	1.0790	-0.9210
1476.7842	13.84	0.0535	1.0535	-0.9465
1476.7878	13.91	0.0418	1.0418	-0.9582
1476.7904	13.94	0.0333	1.0333	-0.9667
1476.7931	14.00	0.0245	1.0245	-0.9755
1476.7956	14.03	0.0163	1.0163	-0.9837
1476.7981	14.07	0.0082	1.0082	-0.9918
1476.8006	14.07	0.0000	1.0000	-1.0000
1476.8033	14.07	0.0088	1.0088	-0.9912
1476.8060	14.05	0.0176	1.0176	-0.9824
1476.8086	14.01	0.0261	1.0261	-0.9739
1476.8111	13.98	0.0343	1.0343	-0.9657
1476.8137	13.93	0.0428	1.0428	-0.9572

Note: R signifies red magnitude

Figure 4. Original light curve plotted with period 0.15315 JD.

Figure 5. Second light curve plotted. Period doubled to 0.3063 to show different minima.

Figure 6. Light curve of RZ Tauri W UMa eclipsing binary star published March, 1999. From A Photometric Study of the W UMa-type system RZ Tauri, by Djurasevic G, Zakirov M, Erkapic S, 1999, Astronomy And Astrophysics. 343: (3) 894-898.

The following is my proposed explanation for variable N’s slight change in magnitude. Assuming N is an eclipsing binary, its very short period of almost seven and a half hours would imply a contact system with a mass transfer. One star would be slightly smaller and dimmer than its cousin. When these two stars are side by side as seen from Earth (see Figure 7, Position 1; also see Figure 5, first maximum), the variable is at maximum magnitude because both stars are in full view and contributing the most light (the visual illustrations of the positions described herein follow this paragraph). As time passes, however, the slightly brighter and bigger star starts to move in front of its cousin (see Figure 7, Position 2; also see Figure 5, midpoint between first maximum and first minimum) and finally completely eclipses the dimmer star (see Figure 7, Position 3; also see Figure 5, first minimum). As the orbit continues (see Figure 7, Position 4), both stars appear side by side once more (see Figure 7, Position 5; also see Figure 5, second maximum), giving another maximum at the same magnitude. The orbit continues as the dimmer star now begins to move in front of its brighter and bigger partner (see Figure 7, Position 6; also see Figure 5, midpoint between second maximum and second minimum), until it finally passes in front of the brighter star (see Figure 7, Position 7; also see Figure 5, second minimum). Because the other star is slightly bigger and they are so close together, the brighter star is not entirely hidden by its cousin, and thus part of the light from the brighter star contributes to the variable’s luminosity. This occurrence makes the variable’s apparent brightness dimmer by about 0.04 magnitudes. Following the cycle, the brighter star again emerges (see Figure 7, Position 8) and both stars appear in the original position, signifying one full rotation (see Figure 7, Position 9).

Figure 7. Proposed positions of variable N, viewed as an eclipsing binary, as each star rotates around its companion.

7. Conclusion

The general appearance of the light curve in Figure 5 suggests an eclipsing binary of system type W Ursae Majoris. For this variable to have such a small period, 0.3063 days, there must be two, egg-shaped stars in contact with each other. Due to the slight change in magnitude, one star must be slightly dimmer and smaller than its neighbor.

The current data disproves my original hypothesis that I would find an intrinsic variable with a period of one or two weeks, and is very much in favor of a binary star system with a period of only seven hours and twenty-one minutes (0.3063 days). Never-theless, I cannot form a definite conclusion until further images are taken to measure the color indexes and to see if the light curve changes over a longer period of time.

8. References

Benbow, W. R.; Mutel R.L. (No date). Eclipse Observations of EQ TAU, [Online].
Available: http://inferno.physics.uiowa.edu/papers/eq-tau.html [1999, November].
Bruton, Dan. (No date). Eclipsing Binary Stars, [Online]. Available:
http://www.physics.sfasu.edu/astro/binstar.html [1999, November].
Djurasevic G, Zakirov M, Erkapic S. 1999, A Photometric Study of the W UMa-type
system RZ Tauri. Astronomy and Astrophysics. 343: (3) 894-898.
Henden, Arne. (No date). U.S. Naval Observatory Flagstaff Station Anonymous FTP
Server, [Online]. Available: ftp://ftp.nofs.navy.mil/pub/outgoing/aah/fastt1/ [1999, August].
Koehn, Bruce. (No date). Astronomical Reference Network REFNET, [Online].
Available: http://asteroid.lowell.edu/cgi-bin/koehn/webnet [1999, September].
MIRA AP User’s Guide (Version 5.0, Revision 1). 1998, Axiom Research, Inc.