Two New Close Binary Central Stars of Planetary Nebulae from a Critically Selected Southern Hemisphere Sample Todd C. Hillwig (Georgia State University) Abstract I present the results of time-resolved photometry of a selection of central stars of planetary nebulae. The study reveals periodic variability in two of the eight central stars observed, those of NGC 6026 and NGC In both cases, the variability shows very little scatter from a sine curve. This variability matches that expected from a binary system in which a hot primary irradiates a cooler secondary star. The small scatter leads to the conclusion that both central stars are not contact or semi-detached systems, but have detached components with a visible irradiation effect. The results of period analysis give orbital periods of days for NGC 6026 and days for NGC The short orbital periods lead to the conclusion that both systems passed through a common envelope phase prior to ejection of the planetary nebula. Limits are also placed on the companion star characteristics. I also discuss the observed binary fraction in relation to the selection criteria and to binary fractions from past photometric studies. Introduction Soker (1997) explained planetary nebula (PN) structures using orbital interactions in a binary system, with the companion to the PN progenitor being either stellar or substellar (brown dwarf or planet). Using this theory he classified a large number of PNe, based on their morphology, as either: single progenitor, close stellar companion with no common envelope (CE) phase, close stellar companion with a CE phase, or substellar companion with a CE phase. These predictions provide a good basis for testing the binary theory of PN shaping. Based on population synthesis calculations by, e.g. Yungelson et al. (1993), it is apparent that for close stellar companions undergoing a CE phase, a significant fraction should become systems with orbital periods on the order of a few days or less. For mid- to late spectral type companions, these systems should then exhibit a “reflection effect” from the irradiated hemisphere of the companion that faces the hot subdwarf. To date thirteen central stars of planetary nebulae (CSPNe) have been identified as close binaries, with orbital periods determined to be < 16 days (Bond 2000). Twelve of the thirteen show variability from either reflection effects or eclipses or both. All of these twelve exhibit orbital periods of < 3 days. Bond (2000) gives the fraction of detectable close binaries from a random sample as  10-15%. I undertook a photometric study of eight southern hemisphere CSPNe classified by Soker (1997) as having a stellar companion that underwent a CE phase. Based on the above information, I expected to find at least one close binary CS. However, if the predictions of Soker (1997) were accurate, I could expect to find a larger fraction of close binaries than the 10-15% expected from a random sample. Here I present the use of time resolved photometry of CSPN to search for the sinusoidal variations in brightness that would be associated with an irradiated hemisphere of a stellar companion to the central star. The results support the classification of NGC 6026 and NGC 6337 as close binary stars. I present orbital periods for these systems. The detected binary fraction is also compared to those discovered in previous studies. NGC 6026 The light curve of NGC 6026 (Figure 1) shows obvious variability and suggests a well-behaved periodic nature. Figure 1 - The light curve of the central star of NGC The immediate appearance of the periodogram for NGC 6026 showed periodic variability with a strong one day alias. The highest peak was located at a period of days. However, the combination of the window function of the data with the one day aliases exaggerates the power of this peak. Folding the data on a period of days shows obvious deviations from smooth variability. The second highest peak however, at days, shows a much closer agreement to a sine curve. This period was taken as a starting point for fitting a sine curve of the form V = V mean + K sin[2  (T-T o )/P +  ] (1) where V is the instrumental magnitude, K is the semiamplitude, and P is the period; either T o or  is a fitted parameter. For the photometry we fit for T o plus the remaining parameters and set  = The phase shift comes from the physical properties of the system. Typically, phase zero is defined as inferior conjunction of the secondary star (equivalent to primary eclipse in eclipsing systems). In the case of a close binary with an irradiation effect the observed emission originates on the inner hemisphere of the secondary star. Therefore inferior conjunction of the secondary will occur when the inner hemisphere of the cool secondary is facing away from us, or at minimum light. The use of  = 0.75 in the above equation produces an ephemeris with minimum light at phase zero. The derived photometric ephemeris for NGC 6026 is then T= (1) (2)E. (2) Figure 2 shows the light curve folded on this ephemeris and the sine curve fit. The rms variation of the data from the fitted sine curve is magnitude. Figure 2 - The light curve from Figure 1 folded on the derived ephemeris. The resulting parameters from the sine fitting are given in Table 2. NGC 6337 As with NGC 6026, the light curve of NGC 6337 in Figure 3 shows apparently well-behaved periodic variability. Figure 3 - The light curve of the central star of NGC The periodogram showed periodic variability with a strong one day alias. The peak with the most power was located at a period of days. Since NGC 6337 appears as a ring, the nebular background close to the central star is at a minimum, allowing more accurate photometry. This, along with the obvious slope to each night of observation allowed all but the highest peak to be rejected. The corresponding period was taken as a starting point for fitting a sine curve of the same form as Equation 1, for NGC The derived photometric ephemeris for minimum light in NGC 6337 is then T= (5) (3)E. (3) Figure 4 shows the light curve folded on this ephemeris and the sine curve fit. Even with fewer points, a reasonably accurate determination of the orbital period is possible, in part due to the larger amplitude of the variability. The rms variation of the data from the fitted sine curve is magnitude. Figure 4 - The light curve from Figure 3 folded on the derived ephemeris. The parameters from the sine curve fit are given with those of NGC 6026 in Table 2. Table 2 - Photometric Sinewave Fit Parameters Observations The photometric data consist of V-band CCD photometry obtained from 30 April - 4 May, 2002 at the Cerro Tololo Interamerican Observatory (CTIO) 0.9m telescope with the T2K Imager. The observations were carried out such that every object was observed each night for at least one hour and the five-night spacing was altered to reduce as many aliases as possible in the period search algorithm to be utilized. The exposures were reduced using the DAOPHOT package of IRAF, producing raw photometry. The resulting photometry was then analyzed by incomplete ensemble photometry (Honeycutt 1992). The zero points are instrumental magnitudes dependent on the instrumental response of the CTIO 0.9m system. The average systematic errors are dependent on the object brightness and typically fall between  and  mag. Non-systematic errors appeared due to changes in seeing. Spatial variations in the PN brightnesses caused background values to fluctuate, as did small changes in focus of the telescope. The resulting errors were in the range  to  mag. Table 1 gives the maximum change in magnitude,  V max, for each of the six systems which did not show unambiguous variations and the average photometric error for a single observation of each object. Also listed are the number of nights observed and the duration of the longest consecutive observation interval. Four nights of data are used for both NGC 6026 and NGC 6337, though NGC 6026 was observed on all five nights. The data for NGC 6026 from night three was found to be compromised by a slight focus offset. The offset combined with the astigmatism in the CTIO 0.9m telescope caused an ellipticity in the image point- spread function (PSF) of  20%. The combination of irregular nebulosity surrounding the central star (CS) and the elliptical PSF caused an offset in the resulting photometry. Since enough data was obtained on the remaining four nights to determine an orbital period, the night three data was not used. Observations of all other objects, on all nights were checked for the same problem. Only a small number of additional images showed similar issues and in each case the background nebulosity was smooth enough or diffuse enough to not cause an appreciable difference in the photometry. The light curves were used in periodogram, a program which uses the period search technique of Scargle (1982) as modified by Horne & Baliunas (1986). Details and results of the period analysis for both NGC 6026 and NGC 6337 are discussed. Table 1 - Non-Variable * CSPN PN Central Star  V max (mag) Ave. error No. of Nights Observed Max. Duration of Observations (min) He K NGC NGC NS Sp PN Central Star V mean (inst. mag) K (mag) T o (Julian days) P (days) NGC (7)0.087(1) (1)0.2636(2) NGC (1)0.209(3) (5)0.1735(3) Secondary Mass Limits and System Inclinations The short orbital periods of both systems allow several of the binary system parameters to be explored further. Taking the masses of both CSs to be  0.6 M , the average for CSPNe, Kepler's 2nd law gives the binary separation as a function of the secondary mass. Furthermore, since the folded light curves in Figures 2 and 4 show little deviation from a sine curve, as expected for pure irradiation, it is doubtful that significant mass transfer is occurring. It is likely then, that both systems have secondaries which do not fill, or just fill, their Roche lobe. For such small orbital periods, the companion in each system must by a main sequence star, a compact star, or a brown dwarf. The significant reflection effects observed in the two systems suggest then, that the companions are considerably cooler than the subdwarf and so are likely not compact objects. To obtain an upper limit for the secondary masses, I will assume that the secondary star will not fill its Roche lobe under the condition that R 2 (MS)  R L,2, where R 2 (MS) is the main sequence radius of a secondary star of mass M 2, and R L,2 is the volume radius of the Roche lobe of the secondary as defined by Eggleton (1983). Values of R 2 (MS) for M 2  0.5 M  are taken from Gray (1992) and for M 2 < 0.5 M  from Caillaut & Patterson (1990). The above condition for a detached Roche lobe is met for the two systems, according to their corresponding orbital periods and for M 1 = 0.6 M , by M 2 (NGC 6026)  0.8 M  and M2(NGC 6337)  0.3 M . These correspond to binary separations of a(NGC 6026)  1.93 R  and a(NGC 6337)  1.26 R . A few comments may be made about the binary system inclinations as well. The most obvious limitation is provided by NGC Corradi et al. (2000) show that the ring-like structure of NGC 6337 (bottom background) is the narrow waist of a nearly pole-on bipolar PN. The inclination of the PN then must be  15º for the bright inner ring to have no apparent ellipticity. If the binary mechanism for shaping PNe is correct, then the close binary CS must also have i  15º. NGC 6026 does not appear ring-shaped, but as a partial ellipse with a very faint south-east edge (top background). If this PN is what Bond (2000) refers to as a “wedding ring” PN, where the observed ellipse is an inclined equatorial ring, then the inclination must be intermediate and can be roughly determined from the ellipticity of the observed PN. The ellipse measures  32”  42”, giving an inclination of  40º. Once again, if binarity is the major shaping mechanism then this may also be taken as the inclination of the central binary. Observed Binary Fractions Finally, previous studies have found the fraction of detectable close binary CSPN to be  10-15% (Bond 2000) with one study resulting in a binary fraction of only 4.5  4.5% from a sample size of 22 CSPNe (Lutz et al. 1998). The binary fraction obtained in this study is 25%, much higher than previous studies, though the low number of statistics means that the results are reasonably similar. Since the sample observed in this study was not randomly selected, but was based on the classifications of Soker (1997), it would be interesting to increase the number of CSPNe observed, thereby increasing the statistical significance of the sample. If the 25% binary fraction persisted, the binary theory for PN shaping would be strongly supported, specifically the orbital interaction scenario outlined by Soker (1997). This research has been funded by Georgia State University. I would like to thank Bill Bagnuolo, Doug Gies, and Bill Nelson for their generous help and support. Also, Todd Henry and Alberto Miranda for their assistance with the CTIO 0.9m telescope. References Bond, H. E. 2000, in ASP Conf. Series 199, Asymmetrical Planetary Nebulae II: From Origins to Microstructures, ed. J. H. Kastner, N. Soker, & S. A. Rappaport, ASP, San Francisco, p. 115 Caillault, J.-P. & Patterson, J AJ, 100, 825 Corradi, R. L. M., Goncalves, D. R., Villaver, E., Mampaso, A., Perinotto, M., Schwarz, H. E., & Zanin, C. 2000, ApJ, 535, 823 Eggleton, P. P. 1983, ApJ, 268, 368 Gray, D. F. 1992, The Observation and Analysis of Stellar Photospheres, Cambridge Univ. Press, Cambridge, p 431 Honeycutt, R.K. 1992, PASP, 104, 435 Horne, J.H. & Baliunas, S.L. 1986, ApJ, 302, 757 Lutz, J., Alves, D., Becker, A., et al. (the MACHO Collaboration) 1998, BAAS, 192, 5309 Scargle, J.D., 1982, ApJ, 263, 835 Soker, N. 1997, ApJS, 112, 487 Yungelson, L. R., Tutukov, A. V., & Livio, M. 1993, ApJ, 418, 794