V and I Light Curves of TY Bootis

David Rafferty

2002 June 3



Abstract

The W UMa type binary TY Bootis was observed on a single night in V and I with the 0.25 meter Great Ohio Telescope. The observations were timed to cover the primary minimum and one maximum of a single epoch. The period was found to be consistent with the published value of 0.317146 days. In addition, the time of primary minimum was derived and compared to the calculated value, and an O-C was derived for this epoch. A discrepancy was found between this O-C and the most recent O-C trends. Lastly, the V-I color was found to be consistent with no change within errors during the time of observation.

1. Introduction

A large percentage of stars belong to binary systems. In these systems, two stars orbit about their mutual center of mass. Some of these systems are inclined at large angles and eclipses occur when one star passes in front of the other. These systems are known collectively as eclipsing binaries. The eclipses produce dips in the light curve (a plot of magnitude versus time) of the system. Studies of the light curve provide clues to the intrinsic properties of the binary members. For example, from the shape of the light curve and the photometry, one may infer the inclination, mass ratio, orbital radii, and temperatures (see e.g. Yang and Liu, 2001).

   One type of eclipsing binary, in which the component stars are so close together as to be in contact, is known as the W UMa type. In approximately 2/3 of W UMa binaries, the colors in the two minima are redder that those of the maxima (Mauder 1972). This effect is typically between 0.1 and 0.05 magnitudes in B-V. This reddening is due to the unique nature of contact binaries in which the side of the star facing the companion is hotter that the side facing away. The orbital periods of some W UMa binaries are also seen to vary slowly (on the order of 10-7 days yr-1); the period change can be decreasing or increasing (Qian 2001). These changing periods are predicted by some theories of contact binary evolution, but are by no means well understood (Qian 2001). It is therefore of interest to study the color and period properties of W UMa type eclipsing binaries, and it is these properties that are the focus of this study.

   The object of this study is TY Bootis, an 11th magnitude W UMa binary. Time constraints necessitated a short period light curve; therefore, TY Bootis was selected as having the shortest period of any eclipsing binary that has a magnitude between 9-16 and no bright companions. TY Bootis was first identified as an eclipsing binary of the W Uma type by Guthnick and Prager (1926), who measured a period of 0.3173 days. Subsequent studies were performed by Szafraniec (1953), Carr (1972), and Samec and Bookmyer (1987), among others, refining the period to its currently accepted value of 0.317146 days (Milone et al. 1991). TY Bootis is typical of a W UMa system, in that there is a continuous change in luminosity during the cycle and the system is redder during each eclipse (both eclipses are partial).

   The object of this project was to measure the light curve in two bands, V and I, from the point of primary minimum to the point of maximum, and thereby to find the time of primary minimum and to quantify the color change. The length of exposure was set by the need for an accuracy of 20% of the maximum predicted color change (Delta (v-i)) of 0.1 magnitudes. This requirement results in a required accuracy in the measurement of the stars to 0.01 in magnitude (assuming an equal error in each band for TY Bootis and the comparison star). The resulting exposure time, found using the ccdtime task in IRAF, was 15 seconds.

2. Observations

The present observations of TY Boo (RA(2000)=15:00:47, Dec(2000)=35:07:58) were made on 2002 April 26 UT with the 0.25 meter Great Ohio Telescope. Observing conditions were not photometric and slowly degraded throughout the night, beginning with minimal clouds and ending with dense cloud cover. The observations were made with the ST8 CCD camera at a operating temperature of -20 Celsius. All calibration frames (11 zeros, 7 darks, and 3 flats in each filter) were made in the evening before the primary science exposures. A total of 28 exposures each in I and V were obtained, and approximately half of the observations were made through clouds. One observation consists of two averaged exposures in each filter, indexed to the time of the middle of the set of two exposures (see Table 1). The order of the exposures was V-I-I-V. The comparison star used to find the magnitude differences was the same as that designated by Szafraniec (1953) as "f" (RA(2000)=15:00:54, Dec(2000)=35:04:17). The comparison star was chosen as being reasonably close in color and magnitude to TY Boo (Milone et al 1991). Differential extinction corrections were not applied, since the stars are within a few arcseconds of each other. Additionally, the instrumental magnitudes were not transformed to the standard system, since this study relies entirely on differential magnitudes.
Table 1. The V and I observations of TY Bootis, after matching frames were averaged. Magnitude differences are in the sense variable star - companion star.

3. Reductions

The raw images were reduced in the standard way following the process described in Masey (1997). The zero frames were combined into a single frame, as were the dark frames. The resulting combined zero was used to correct the combined dark for bias level, which was then used, along with the combined zero, to correct the flat field exposures. The object frames were corrected only with a combined dark without zero correction. The flats were then combined (in each filter) and then divided out of the object frames. An inspection of the resulting object frames verified the success of the reductions.

   The instrumental magnitudes of TY Boo and the comparison star were found using aperture photometry with the IRAF task phot of the noao.digiphot.daophot package. The phot task calculates the magnitude inside a specified aperture, subtracting a local sky value from an annulus around the star. The point spread functions of the two stars (TY Boo and the comparison star) were examined and the average HWFM was found to be approximately 4 pixels for frames without clouds. The aperture was set to four times the HWFM or 15 pixels, with the sky annulus at an inner radius of 20 pixels and a width of 5 pixels. The phot task was then run on each frame and the instrumental magnitudes and the associated errors of the two stars were recorded.

4. Results

Once the magnitudes of TY Bootis and the comparison star were obtained, the magnitude differences were calculated by first subtracting, in each frame, the magnitude of the comparison star from that of TY Boo. For each observation (consisting of two frames in V and two in I), the magnitude differences were averaged and indexed to a time in the middle of the two frames. For the V-I color light curve, the color differences were found for each neighboring set of V and I frames and then averaged with the remaining V and I frames of the observation set (V-I-I-V). In all cases, errors were assumed to be independent and random and were added in quadrature. The final light curves are shown in Figure 1.
Figure 1. Light curves of TY Bootis. Top: the V-I color light curve. Middle: the V-band light curve. Bottom: the I-band light curve. All magnitude differences are in the sense variable star - comparison star.

   The light curves of Figure 1 show the variable nature of TY Bootis, with both the primary and secondary minima clearly discernible to the left and right of the maximum in the V and I plots. A first order approximation to the period was found by measuring the time between the points with greatest magnitude change in the two minima. The derived period is 0.30±0.05 days.

   The effects of increasing cloudiness are apparent in the worsening errors of the latter points. In particular, these effects obscure any color change in the V-I light curve. However, the dip in the V and I light curves at primary minimum is clear, and a fit was obtained to those five data points to determine the time of primary minimum (see Figure 2).
Figure 2. V and I light curves showing best fit quadratics. The time of primary minimum (JD = xmin + 2452390)) is shown below the equation.

   The fits were weighted quadratic regressions (of the from y = A1 + A2 x + A3 x2) with the coefficients shown in Table 2.
Table 2. Results of the weighted quadratic regressions.

The derived time of primary minimum is slightly different in V (JD=2452390.7778±0.0007) and I (JD=2452390.7789±0.0033). The average of these values was used as the best estimate of the time of primary minimum:

JD Hel. Min. I = 2452390.778±0.002.

Additionally, the point of primary minimum is defined as zero phase; therefore, the time axis may be transformed to phase. Figure 3 is a phase plot of the V light curve with the V light curve of Carr (1972) overlaid for reference. The light curve of Carr has not been scaled or shifted vertically, though some shift is probably appropriate due to differing telescope response.
Figure 3. V light curve with the V light curve of Carr (1972) overlaid (dashed line). The point of zero phase is defined to be the time of primary minimum.

With the published ephemeris of Samec and Bookmeyer (1987):

JD Hel. Min I = 2446589.7906 + 0.31714964 E,

where E is phase, the time of primary minimum may be used to calculate the O-C (observed - calculated) for this epoch (E = 18291):

O-C (present study) = 0.003±0.002 days.

5. Discussion

The O-C of the present study may be compared with previous studies to look for long term period changes. Figure 4 presents all the published O-C's (taken from Rainger et al. 1990 and Qian 2001), calculated with the ephemeris given in section 4. The points on Figure 4 are differentiated by type of observation: visual, photographic, or photoelectric.
Figure 4. O-C curve for TY Boo. All present and published data are shown.

   An early trend is apparent in the figure in the visual data, which suggests that the period of TY Boo decreased (as the O-C's decreased). There is also a clear trend in the most recent photoelectric data suggesting that the period of TY Boo is now slowly increasing. The O-C of the present study does not fit this trend. This mismatch leads to two possible conclusions:
  1. The period of TY Boo is again decreasing
  2. The O-C of the present study is in error.
The second conclusion is the most likely when taking into consideration the relatively poor quality of the data of this study compared to previous photoelectric studies. In particular, a positive determination of the time of primary minimum necessitates two or more samples of the light curve from two different epochs; this study observed only one epoch. The result that the O-C of this study is inconsistent with recent trends implies that one or more points used for the best fit curve presented in section 4 are incorrect. Figure 4 suggests that the O-C should be on the order of 0.015, requiring a shift of the time of minimum to the right (toward later times). The data of Carr was shifted to achieve to lowest reduced chi-squared with the present data. When all points are included, the best reduced chi-squared is 29. However, if two points are removed, the fifth (at a phase of 0.02 on Figure 5) and twelfth (at a phase of 0.80), a reduced chi-squared of 0.6 is achieved with a shift of 0.0072 days in x and 0.053 magnitudes in y (see Figure 5).
Figure 5. V light curve for TY Boo, with the light curve of Carr (1972) overlaid with a shift in x (0.0072 days = 0.0227 in phase) and y (0.053 mag) (dashed line).

   The reason for the discrepancies in these two points is not clear. No short term effect (on the order of a single exposure) can account for this effect, as the points are also deviant in the I light curve and therefore over at least four exposures or approximately 8 minutes. Inspection of the images did not reveal any anomalies not present in many other exposures. However, the chosen aperture of 15 pixels may not have been appropriate for every image. Probably, however, a concatenation of circumstances led to the bad data points.

   The O-C for the chi-squared fit to Carr's data is:

O-C (present study) = 0.011±0.009 days.

This new value is shown on Figure 6.
Figure 6. O-C curve for TY Bootis with revised datum.

This revised value agrees reasonably well with the earlier photometric values, but the errors are large enough that it does not constrain the present trend in the period, which may be increasing or decreasing.

   Lastly, the derived period of 0.3±0.05 days is consistent with the most recent published value of 0.317146 days (Milone et al. 1991), and the total color change in V-I is consistent with the published value from Milone et al 1991 of approximately 0.1 magnitudes. In conclusion, the data obtained are consistent with, but do not place any real constraints on, recent published values of the period, O-C, and color change. Photometric conditions and multiple nights of observations would result in more useful data.

References

Carr, R. B. 1972, AJ, 77, 155
Guthnic, P. & Prager, R. 1926, Astron. Nachr., 228, 99
Massey, P. 1997, A User's Guide to CCD Reductions with IRAF
Mauder, H. 1972, A&A, 17, 1
Milone, E. F., Groisman, G., & Fry, D. J. I. 1991, ApJ, 370, 677
Qian, S. 2001, MNRAS, 328, 635
Rainger, P. P., Hilditch, R. W., & Bell, S. A. 1990, MNRAS, 246, 42
Samec, R. G. & Bookmyer, B. B. 1987, PASP, 99, 842
Szafraniec, R. 1953, Acta Astron., Ser. b, 2, 86
Yang, Y. & Liu, Q. 2001, AJ, 122, 425