THE CASE FOR THIRD BODIES AS THE CAUSE OF PERIOD CHANGES IN SELECTED ALGOL SYSTEMS

Transcription

1 The Astronomical Journal, 132:2260Y2267, 2006 December # The American Astronomical Society. All rights reserved. Printed in U.S.A. THE CASE FOR THIRD BODIES AS THE CAUSE OF PERIOD CHANGES IN SELECTED ALGOL SYSTEMS D. I. Hoffman, 1 T. E. Harrison, 1 B. J. McNamara, 1 W. T. Vestrand, 2 J. A Holtzman, 1 and T. Barker 3 Received 2006 May 1; accepted 2006 August 14 ABSTRACT Many eclipsing binary star systems show long-term variations in their orbital periods, evident in their O C (observed minus calculated period) diagrams. With data from the Robotic Optical Transient Search Experiment (ROTSE-I) compiled in the SkyDOT database, New Mexico State University 1 m data, and recent American Association of Variable Star Observers ( data, we revisit Borkovits and Hegedüs s best-case candidates for third-body effects in eclipsing binaries: AB And, TV Cas, XX Cep, and AK Her. We also examine the possibility of a third body orbiting Y Cam. Our new data support their suggestion that a third body is present in all systems except AK Her, as is revealed by the sinusoidal variations of the O C residuals. Our new data suggest that a third body alone cannot explain the variations seen in the O C residuals of AK Her. We also provide a table of 143 eclipsing binary systems that have historical AAVSO O C data with new values computed from the SkyDOT database. Key words: binaries: eclipsing stars: individual (AB Andromedae, TV Cassiopeiae, XX Cephei, AK Herculis, Y Camelopardalis) 1. INTRODUCTION Many eclipsing binary star systems show long-term variations in their orbital periods. These changes are typically displayed in an O C (observed minus calculated period) plot in which the differences in their observed times of eclipse minima and those predicted by their original ephemeris are plotted as a function of Julian Date. If the binary period is constant, this plot shows a straight line at O C ¼ 0. If the O C variations follow a straight line with a nonzero slope, then the assumed period is likely to be incorrect. A sinusoidal-like O C pattern may be caused by the precession of the orbit (apsidal motion) or the presence of a third body. Many systems have an even more complex O C diagram in which the cause of these variations remains a mystery. All of these different patterns are seen in the O C diagrams of the Algol, RS Canum Venaticorum, and W Ursae Majoris systems. Therefore, it is important to explain their origin. This paper concentrates on the systems in which the O C variations follow a sinusoidal pattern. Apsidal motion, the change in the projected orbit along our line of sight associated with eccentric orbits, provides a natural explanation for the presence of a sinusoidal pattern in the O C diagram of a binary. However, the orbital eccentricity for most close binaries (such as W UMa stars) is thought to be very small, and therefore apsidal motion should not be present. In addition, even when a sinusoidal pattern is seen, the observed primary and secondary minima usually lead to identical O C plots. Since the projected separation within the binary changes in an elliptical orbit, the separation in time between the primary and secondary minima are not constant. Thus, if apsidal motion is present, the primary and secondary minima will, in general, not give identical O C plots. An alternative explanation for this type of pattern is that the system consists of a close binary orbited by a distant third body. The third body then produces a light-time effect (LITE) as the two components in the shorter period binary orbit the center 1 Department of Astronomy, New Mexico State University, Box 30001, MSC 4500, Las Cruces, NM 88003; dhoffman@nmsu.edu, tharriso@nmsu.edu, bmcnamar@nmsu.edu, holtz@nmsu.edu. 2 Los Alamos National Laboratory, Los Alamos, NM 87545; vestrand@lanl.gov. 3 Department of Physics and Astronomy, Wheaton College, Norton, MA 02766; tbarker@wheatoncollege.edu. of mass of the triple system. The LITE produces a smoothly varying sinusoidal change in orbital period. An alternate cause of sinusoidal O C variations is suggested by the work of Hall (1989). Nearly two decades ago, he proposed that magnetic activity in late-type binary secondaries plays a role in inducing period changes. He found that in a sample of 101 Algols, none exhibited period changes of alternating sign when the secondary star had a spectral type earlier than F5. Stellar models suggest that this spectral type is close to the boundary where the onset of convection occurs. This correlation between a change in sign of the slopes in the O C curves and the development of surface convection zones in main-sequence stars has caused some researchers to speculate that these two phenomena are physically connected. Applegate (1992) and Lanza et al. (1998) suggest that during a stellar cycle, magnetic activity and convection in a late-type secondary transport angular momentum toward the surface of the star. This process changes the star s oblateness, creating a quadrupole moment in its gravitational potential that alters the system s orbital period. Zavala et al. (2002) reexamined the correlation found by Hall using updated light curves and spectral-type data for 66 Algols. They found that Algols with secondary stars later than type F5 possessed large O C variations, while those with hotter companions did not. This result suggested that there might be a correlation between magnetic activity and the size of the O C variations. Borkovits & Hegedüs (1996, hereafter BH96) have identified five Algol systems AB And, TV Cas, XX Cep, AK Her, and Y Cam that appear to possess a sinusoidal pattern in their O C diagrams. BH96 consider the first four systems to be the best candidates for testing the third-body hypothesis. Y Cam is identified by BH96 as a more problematic case, yet we still investigate it, as it possesses a clear sinusoidal variation in its O C plot, which is indicative of a third body. If new O C observations show that the sinusoidal pattern is continuing, the third-body hypothesis is viable. If the pattern is not maintained, the O C variations cannot be solely explained by the presence of a third body. In addition to examining this question, we also present O C values for 143 other binaries that can be used in studies of their O C plots. 2. OBSERVATIONAL DATA The O C values used in this study were collected from a number of sources. The vast majority of the new values were 2260

2 Star TABLE 1 ROTSE-I O C Data Period (days) Epoch 2,400,000+ Mean HJD 2,450,000+ O C (days) Light Curve Type Spectral Type References AB And , , W UMa G5+G5 8, 9 AB Cas , , Algol A3+K 8, 9 AC Tau , , Algol F0+K6 4, 10 AD And , , Algol... 3 AD Boo , , Algol G0+ 4, 9 AE Cyg , , Algol A5+F0 3, 10 AF Gem , , Algol A0+G1 3, 10 AH Vir , , W UMa K2+ 7, 9 AK CMi , , Algol A3+K2 4, 10 AL Cam , , Algol A2+ 2, 9 AL Gem , , Algol F5+K7 6, 10 AO Ser , , Algol A2+G5 6, 10 AT Mon , , Algol... 6 AV Hya , , Algol... 1 AW Vul , , Algol F0+K1 IV 5, 10 AY Vul , , Algol F0+K0 IV 6, 10 AZ Vir , , W UMa... 8 BB Peg , , W UMa F8+ 8, 9 BD And , , Algol... 3 BE Vul , , Algol A0+ 4, 9 BH Dra , , Algol A2+ 2, 9 BH Vir , , RS CVn F8+ 3, 9 BO Vul , , Algol F0+G0 IV 5, 10 BR Cyg , , Algol A5+F0 V 8, 10 BS Vul , , Algol... 6 BT Vul , , Algol... 6 BU Vul , , Algol... 7 BX And , , W UMa F2V+ 7, 9 CC Com , , W UMa... 7 CC Her , , Algol A0+G6 IV 3, 10 CD Vul , , Algol F2+ 3, 9 CG Cyg , , Algol G9.5+K3 V 8, 10 CM Lac , , Algol A2 6, 10 CT Her , , Algol A3+G3 IV 7, 10 CT Tau , , W UMa... 2 CW Cas , , W UMa... 8 CX Aqr , , Algol F2+ 7, 9 CZ Aqr , , Algol A5+G3 IV 3, 10 DF Hya , , W UMa... 8 DK Cep , , Algol... 5 DK Cyg , , W UMa A6+ 8, 9 DK Hya , , Algol... 8 DL Cep , , Algol B+ 8, 9 DS And , , Algol... 7 DZ Cas , , Algol... 7 EG Cep , , Algol A3+ 5, 9 EP Aur , , Algol... 2 EP Mon , , Algol... 4 EQ Ori , , Algol A0+G2 IV 7, 10 EQ Tau , , W UMa... 7 ER Ori , , W UMa F8+ 7, 10 ET Ori , , Algol G3+K3 IV 3, 10 FZ Del , , Algol F5+K4 IV 8, 10 GP Peg , , Unclassified... 8 GU Ori , , Algol... 8 HP Aur , , Unclassified... 8 IR Cas , , Algol... 6 IV Cas , , Algol A2+G1 V 4, 10 KP Aql , , Algol A3+ 6, 9 KR Cyg , , Algol A0+ 5, 9 KW Per , , Algol... 5 MM Cas , , Unclassified... 2 OO Aql , , W UMa G5+ 7, 9 OR Cas , , Algol... 2

3 Star TABLE 1 Continued Period (days) Epoch 2,400,000+ Mean HJD 2,450,000+ O C (days) Light Curve Type Spectral Type References OX Cas , , Unclassified B1 V 3, 9 RR Lep , , Algol A0+ 3, 9 RS Tri , , Algol A5+ 3, 9 RT And , , RS CVn F8+ 7, 9 RT Per , , Algol F5+G0 6, 10 RU Mon , , Algol B9+ 6, 9 RU UMi , , Algol F0+K5 8, 10 RV Crv , , Unclassified F0+ 6, 9 RV Per , , Algol A2+M0 IV 2, 10 RV Psc , , Algol... 5 RV Tri , , Algol F9+K2 6, 10 RW Cap , , Algol A2+ 5 RW Gem , , Algol B5+F5 3, 10 RY Lyn , , Unclassified... 2 RZ Com , , W UMa G0+ 7, 9 RZ Dra , , Algol A5+K2 IV 8, 10 SS Ari , , W UMa... 4 SS Lib , , Algol A5+F5 5, 10 ST Per , , Algol A3+G8 IV 7, 10 SU Cep , , Algol... 3 SV Cam , , Unclassified G5+ 7, 9 SW Lac , , W UMa K0+ 8, 9 SX Oph , , Algol... 4 SZ Her , , Algol A/B+BYG 7, 10 TT Del , , Algol A1+G7 IV 3, 10 TU Boo , , W UMa... 8 TU Her , , Algol F5+M1 8, 10 TW And , , Algol F0+K0 6, 10 TW Cet , , W UMa G5+G5 7, 9 TY Boo , , W UMa... 8 TY Del , , Algol B9+G0 IV 7, 10 TY Peg , , Algol A2+G5 IV 2, 10 TZ Boo , , W UMa G2+ 8, 9 TZ Eri , , Algol F3+K5 IV 6, 10 U Peg , , W UMa G2+ 7, 9 UU And , , Algol F5+K6 IV 8, 10 UU CMa , , Algol... 3 UU Leo , , Algol A2+G1 V 5, 10 UX Her , , Algol A3+GYK 3, 10 UX UMa , , Unclassified... 5 UZ Dra , , Algol F8+ 7, 9 UZ Lyr , , Algol A0+K1 IV 7, 10 UZ Pup , , Algol A6+A6 8, 9 V346 Aql , , Algol A0+G4 IV 8, 10 V364 Cas , , Algol... 4 V387 Cyg , , Algol... 7 V388 Cyg , , Algol... 7 V456 Cyg , , Algol... 4 V466 Cyg , , Algol... 4 V704 Cyg , , W UMa... 6 V Crt , , Algol A6+ 3, 9 V Tri , , Algol A3+F6 8, 10 VV UMa , , Algol A2+G1 IV 7, 10 VV Vir , , Algol... 3 VW Boo , , W UMa G5+ 4, 9 VX Lac , , Algol F0+K4 IV 7, 10 VZ Leo , , Algol A5+G7 IV 8, 10 W Crv , , Algol... 7 WW Cyg , , Algol B7+G1 IV 2, 10 WY Hya , , Algol... 7 WY Tau , , W UMa... 4 WZ Cep , , W UMa... 3 X Tri , , Algol A3+G3 IV 7, 10 XX Cep , , Algol A8+G4 IV 8, 10 XZ And , , Algol A4+G2 IV 6, 10

4 THIRD BODIES AND PERIOD CHANGES IN ALGOLS 2263 TABLE 1 Continued Star Period (days) Epoch 2,400,000+ Mean HJD 2,450,000+ O C (days) Light Curve Type Spectral Type References XZ Aql , , Algol A2+F8 2, 10 XZ CMi , , Algol... 8 XZ Per , , Algol G1+K1 IV 7, 10 XZ UMa , , Algol A5+G4 IV 6, 10 Y Cam , , Algol A7+K5 IV 3, 10 Y Leo , , Algol A3+K6 IV 5, 10 Y Psc , , Algol A4+K0 IV 8, 10 YY Del , , Algol... 6 Z Dra , , Algol F4+G8 IV 8, 10 Z Lep , , Algol F0+F2 8, 10 Z Per , , Algol A0+G2 IV 3, 10 ZZ Cep , , Algol A2+ 1, 9 ZZ Cyg , , Algol F7+K5 IV 6, 10 ZZ UMa , , Algol F8+ 4, 9 References. (1) Baldwin & Samolyk 1993; (2) Baldwin & Samolyk 1995; (3) Baldwin & Samolyk 1996; (4) Baldwin & Samolyk 1997; (5) Baldwin & Samolyk 1999; (6) Baldwin & Samolyk 2000; (7) Baldwin & Samolyk 2002; (8) Baldwin & Samolyk 2003; (9) Kharchenko 2001; (10) Budding et al acquired from observations obtained by the Robotic Optical Transient Search Experiment ( ROTSE-I; Akerlof et al. 2000) and archived in the SkyDOT database 4 (Woźniak et al. 2004). ROTSE-I consisted of four Canon 200 mm lenses mounted on a single platform. Its combined field of view was about 16 ; 16 deg 2,witha limiting magnitude of 15 and a saturation magnitude of 9.5 in unfiltered light. While awaiting notification of the detection of a gamma-ray burst by Earth-orbiting satellites, it acquired twicenightly unfiltered images of the entire northern sky. The initial data from ROTSE-I were released as the Northern Sky Variability Survey (NSVS) in 2004 (Woźniak et al. 2004) and include digital sky images obtained from 1999 April 1 to 2000 March 30. Star positions in the NSVS catalog have errors of 0N3, and blending normally occurs inside The NSVS database consists of about 2 Tbytes of data with 225,000 separate images. Photometric calibration images were taken each night. Field-flattened images were then passed through a photometric reduction routine called SExtractor ( Bertin & Arnouts 1996) that produced magnitudes for about 14,000,000 objects. This study also employs older O C values from the American Association of Variable Star Observers (, compiled by Baldwin & Samolyk (1993, 1995, 1996, 1997, 1999, 2000, 2002, 2003). The ephemerides from the AAVSO publications were also used to phase the data, as well as to examine historical changes in the O C data. In addition, light-curve data from the late D. Lichtenknecker, kindly provided by T. Borkovits (2005, private communication), as well as data from the New Mexico State University (NMSU) 1 m telescope, were also employed. Of the 155 targeted eclipsing binaries, 118 are Algols, 29 are W UMas, and 8 are still unclassified. 3. ANALYSIS METHOD To compute O C values we first phased the ROTSE-I data to the published AAVSO orbital period for each system. We then used IRAF s SPLOT package to fit a Gaussian to the primary eclipse, which provided the phase offset at minimum. Since the predicted primary eclipse occurs at phase 0, this offset is simply the phase calculated at primary minimum. Multiplying the offset by the orbital period gives the O C value. This procedure was used because nightly data points did not provide adequate coverage of the minima. The effective dates for the new O C values are given as 4 Available at the average of the first and last observation with ROTSE-I (typically a 1 yr span). Since the periods of these binaries change very little in 1 yr, this method produces reliable O C values. We were successful in extracting 143 new O C values for these objects. Too few data points were found for nine objects to calculate this value. Of the 143 successful extractions, 110 are Algols, 25 are W UMas, and 8 are unclassified. The new O C values for these systems are listed in Table 1. Since the primary goal of this paper is to test whether the thirdbody candidates provided by BH96 continue to follow the sinusoidal variations revealed by their analysis, we used the same analysis approach they employed. Following their prescription, a least-squares line or parabola was initially subtracted from the entire O C data set for each of the four best-case third-body candidate systems: AB And, TV Cas, XX Cep, and AK Her. In the case of Y Cam, the third body is assumed to be evident in the raw O C plot; thus, no subtraction was made in the third-body analysis, although we subtract a sinusoidal fit to explore the possibility of a fourth body, suggested by Mossakovskaya (1993b). Subtracting a line is equivalent to making a correction in the historical orbital period. Subtracting a parabola adjusts the O C curve for a linearly increasing or decreasing period. Neither of these patterns would be created by a LITE. The presence of a third body is then inferred by a sinusoidal variation in the O C residuals due to a LITE. To compute the orbital parameters of the third body for each system, we followed the procedure of BH96 and Kopal (1978). Using the discrete Fourier transformation ( DFT) method, approximate frequency harmonics and amplitudes were identified. The next step is to fit a curve of the following form to the data: O C(t) ¼ 0:5a 0 þ X2 k¼1 ½a k sin (2kt=P 0 ) þ b k cos (2kt=P 0 ) Š; ð1þ by least-squares fitting using the values from the DFT as initial guesses. The orbital parameters can then be computed from the Fourier coefficients ( Kopal 1978) as follows: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a 0 sin i 0 ¼ c a 2 1 þ b2 1; ð2þ e 0 ¼ 2 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a 2 2 þ b2 2 a 2 1 þ ; b2 1 ð3þ

5 2264 HOFFMAN ET AL. Vol. 132 Fig. 1. O C diagram (top) and residuals (middle) for AB And obtained by subtracting a least-squares parabola (solid line). The bottom panel shows the residuals obtained by subtracting the LITE solution (middle, solid line). The dotted line indicates the end of the data BH96 used. where a 1;2 and b 1;2 are the Fourier coefficients, a 0 is the semimajor axis of the absolute orbit of the center of mass of the eclipsing pair around that of the triple system, i 0 is the inclination of the third body, e 0 is the eccentricity of the long-period orbit, and c is the speed of light. The mass function is determined by the following formula (BH96): f (m 3 ) ¼ 42 a 03 sin 3 i GP 02 ; ð4þ where G is the gravitational constant and P 0 is the period of the third body determined by the DFT method. 4. RESULTS In this section we discuss the four best-case third-body candidates presented by BH96: AB And, TV Cas, XX Cep, and AK Her. We also discuss the possibility that Y Cam possesses a third body, which BH96 identified as a more problematic case. It should be noted that in Figures 1Y4, the top panel shows the raw O C data, the middle panel shows the residuals from subtracting the solid line of the top panel, and the bottom panel shows the residuals from subtracting the solid line of the middle panel. The solid line in the middle panel shows the fit derived by the method described in x 3. No subtraction was necessary for Y Cam (Fig. 5); thus, that figure only has two panels, with the raw O C data and sinusoidal fit in the top panel and the residuals from subtracting that fit in the bottom panel. In BH96 the residuals are presented in the top panel, while the bottom panel shows the secondary residuals of their third-body fit. The solid lines in the top panels of our figures are not meant to be a model (except for Fig. 5) but merely a guide to show what was subtracted to obtain the residuals in the bottom panels. The least-squares fitting routine described in x 3 is very sensitive to the initial guesses. In many cases a small change in the initial guesses yielded vastly different orbital parameters. The eccentricity varies the most on a change of the initial guesses, while the other parameters seem to be more stable. Our results show that Fig. 2. O C diagram (top) and residuals (middle) for TV Cas obtained by subtracting a least-squares parabola (solid line). The bottom panel shows the residuals obtained by subtracting the LITE solution (middle, solid line). The dotted line indicates the end of the data BH96 used. the addition of new data has, in some cases, radically changed the orbital parameters from those determined by BH96. Table 2 compares the values of P 0, e 0, a 0 sin i, and the mass function f (m 3 ) derived by BH96 with those derived by the present paper. Errors for each value are not given, since we have less than one cycle of the oscillations to work with in some cases. More data are required to adequately determine the errors AB And This W UMa binary has an orbital period of 0.33 days. BH96 subtracted a least-squares parabola from its O C diagram and Fig. 3. O C diagram (top) and residuals (middle) for XX Cep obtained by subtracting a least-squares line (solid line). The bottom panel shows the residuals obtained by subtracting the LITE solution (middle, solid line). The dotted line indicates the end of the data BH96 used.

6 No. 6, 2006 THIRD BODIES AND PERIOD CHANGES IN ALGOLS 2265 Fig. 4. O C diagram (top) and residuals (middle) for AK Her obtained by subtracting a least-squares line (solid line). The bottom panel shows the residuals obtained by subtracting the LITE solution (middle, solid line). The dotted line indicates the end of the data BH96 used. found a sinusoidal variation in the residuals. Their analysis showed that these variations could be explained by a third body with a period of 19,765 days, an eccentricity of 0.14, and a mass function of M. Since the first and last data points used by BH96 covered 24,240 days, only one cycle was present in their O C diagram. However, with the new data, which cover 28,794 days, it is possible to see more than one cycle and thus better determine the period of the third body. Since the O C patterns of eclipsing binaries are often highly variable, it is possible that the segment used by BH96 does not reflect the true long-term behavior of AB And. Newer O C values, separated by 11 yr from the last O C point available to BH96, were obtained to test whether the sinusoidal pattern continues to be present. If not, the third-body hypothesis is difficult to maintain. Our new O C data for AB And include one measurement with the NMSU 1 m, a time-averaged ROTSE data point, and new AAVSO data. These new data reveal that the O C pattern (Fig. 1, top panel), which was declining, is beginning to turn around again. After subtracting the least-squares parabola from the O C data, the residuals (middle panel) show a sinusoidal pattern. Our fit (solid line, middle panel) was subtracted, yielding the residuals in the bottom panel. Our new data and analysis suggest that the third body has a period of 19,046 days, an eccentricity of 0.22, and a mass function of M. The new data are consistent with those of BH96. Therefore, our new data support BH96 s claim that a third body is present in this system. However, there is one caveat: the earliest O C points, prior to JD 2,428,000, deviate greatly from that predicted by the sinusoid. These earlier data were derived from photographic observations with exposure times of approximately 45 minutes. The deviation of these older O C values from the sinusoidal fit is about 10 minutes. It is not known how the observed times of minimum were assigned, so it is possible that their O C values may be inconsistently defined with respect to the rest of the data set. However, the overall declining trend in these O C data connects smoothly with the subsequent data points, suggesting that their times are not in error. Since the eccentricity of W UMa stars is very close to unity, Fig. 5. O C diagram (top) and residuals (bottom) for Y Cam obtained by subtracting the LITE solution (solid line). The dotted line indicates the end of the data BH96 used. apsidal motion can be ruled out as the cause of this sinusoidal residual pattern. We conclude that if these early O C values are ignored (as they were in our analysis), AB And remains an excellent case for a three-body system TV Cas This Algol was another of BH96 s best cases for a third body altering the O C curve. The BH96 results suggest that this system contains a third body with a period of 21,412 days, an eccentricity of 0.16, and a mass function of M. Using new and historical AAVSO data, we sought to verify this result. Following BH96 s method, we fit a least-squares parabola to the O C data shown in Figure 2 (top panel ). The residuals (Fig. 2, middle panel) reveal a relatively low-amplitude sinusoidal variation. The new data suggest a new turnover in recent times, allowing further refinement of the third-body period. Our model (Fig. 2, solid line, middle panel) suggests a third body with a period of 24,006 days, an eccentricity of 0.59, and a mass function of M. BH96 did not use data prior to JD 2,427,000, which explains the difference in the derived eccentricities. The other parameters are consistent with those found by BH96. However, the source of the oscillation in the residuals is not clear. It could be due to the light-travel effects of a third body (as we modeled) or to apsidal motion. Both of these could produce this oscillation. Kopal (1978) and Hegedüs (1988) have found systems with similar periods to TV Cas to be apsidal-motion candidates. Therefore, the lack of observations of the secondary minima does not allow apsidal motion to be ruled out XX Cep A third Algol studied by BH96 was XX Cep. BH96 analyzed O C values for XX Cep from approximately JD 2,428,000 to 2,444,000 but excluded the data near the jump at JD 2,435,800 (see Fig. 3, top panel). Additional data were available after JD 2,444,000 but were not analyzed. BH96 found the period of the third body to be 21,888 days, with an eccentricity of 0.26 and a mass function of M. Our analysis used all the data after the period jump at JD 2,435,800. A least-squares line was subtracted from the entire O C data set available to BH96, plus the

7 2266 HOFFMAN ET AL. Vol. 132 TABLE 2 BH96 and Present Paper Third-Body Results AB And TV Cas XX Cep AK Her Y Cam Parameter BH96 Present BH96 Present BH96 Present BH96 Present BH96 Present P e a 0 sin i f (m 3 ) Notes. Solutions for systems in the BH96 paper and the present paper. Here P 0 (in days), e 0,anda 0 sin i (10 6 km) are the orbital elements of the third body, and f (m 3 )is the mass function of the third body (in units of solar mass). new AAVSO and NMSU 1 m O C values. The resulting residuals show a sinusoidal oscillation (see Fig. 3, middle panel). The most recent data show a turnover in the residuals near JD 2,449,000. The new data set suggests that the period of the third body is 15,709 days. Further observations are needed to confirm whether the new turnover is real and to better confirm the period of the third body. Our model (Fig. 3, solid line, middle panel ) also suggests that the possible third body has an eccentricity of 0.33 and a mass function of M. As with TV Cas, apsidal motion cannot be ruled out as the cause of these O C residuals. Further observations of the secondary eclipses are necessary to examine this possibility AK Her AK Her is the last of BH96 s best candidates for a system possessing a third body. Their results suggest that this system contains a third body with a period of 27,243 days, an eccentricity of 0.33, and a mass function of M. AK Her is overexposed on ROTSE-I images, so new AAVSO and NMSU 1 m data were employed to derive recent O C values. After subtracting a leastsquares line to the data shown in Figure 4 (top panel), the residuals were found to deviate from a sinusoid (middle panel). Curiously, the residuals superficially resemble a damped oscillator. Orbital precession of an elliptical orbit coupled with the LITE could produce a beating that may explain the observed pattern in the residuals. Future observations would be extremely valuable in exploring this idea. Our model (Fig. 4, solid line, middle panel) suggests that the third body would need to have a period of 39,053 days, an eccentricity of 2.36, and a mass function of M. Clearly, the model fails, as the third body would be unbound. Our results differ greatly from those of BH96. It is evident that BH96 did not subtract a least-squares line from the raw O C diagram, but it is not clear how they determined the line they subtracted. The choice of this line accounts for the differences in our results. If one extrapolates BH96 s model for AK Her, one would expect the O C data after JD 2,449,000 to become more negative, yet the actual data show the exact opposite. The recent data and our analysis make it clear that the O C variations seen in AK Her cannot be explained solely by the LITE of a third body Y Cam As shown in Figure 5, Y Cam appears to be a textbook case for a three-body system. The O C curve (Fig. 5, top panel) is clearly sinusoidal. BH96 present their results for this star only in a table, in which they list the hypothetical third body as having a period of 50,408 days, an eccentricity of 0.35, and a mass function of 40 M. Although a third body with these parameters might explain the O C residual pattern, they are not physically realistic. A normal star of this mass should be easily seen, since it would outshine the rest of the system. Since we do not see an O star in the system, another explanation is that this object is not a normal star but a relativistic object (Mossakovskaya 1993a). After subtracting our fit (Fig. 5, solid line, top panel), the residuals still possess sinusoid-like components, especially in recent times. Our results show the hypothetical third body having a period of 50,301 days, an eccentricity of 0.38, and a mass function of 34.6 M. Mossakovskaya (1993b) speculated that this system possesses a fourth body, but this secondary residual pattern could also be caused by intrinsic variations, such as gravitational quadrupole moment changes or apsidal motion similar to that proposed for AK Her. Y Cam is also a known Scuti star (Broglia & Conconi 1984), one of a very small number (5) of eclipsing binaries possessing this type of variable star. 5. SUMMARY The ROTSE-I data have proven to be very useful tools for studying period shifts in eclipsing binary systems. The O C data presented in this investigation targeted stars that have existing O C data from the AAVSO. Many more eclipsing systems are in the database but do not have extensive historical records. 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