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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 .
it is understood 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 . to date , thirteen central stars of planetary nebulae ( cspne ) have been identified as close binaries , with orbital periods determined to be @xmath0 days ( bond 2000 ) .
bond ( 2000 ) gives the fraction of detectable close binaries from a random sample as @xmath1 .    here
i present the use of time resolved photometry of cspne to search for the sinusoidal variations in brightness that would be associated with an irradiated hemisphere of a stellar companion to the central star .
eight southern hemisphere cspne classified by soker ( 1997 ) as having a stellar companion that underwent a ce phase were observed .
the results support the classification of ngc 6026 and ngc 6337 as close binary stars .
i present orbital periods for these systems .
my detected binary fraction is also compared to that discovered previously .
the photometric data consist of v - band ccd photometry obtained from 30 april - 4 may , 2002 at the cerro tololo interamerican observatory ( ctio ) 0.9 m 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 .
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 0.9 m system .    the light curves were analyzed with _ periodogram _ , a program which uses the period search technique of scargle ( 1982 ) as modified by horne & baliunas ( 1986 ) .
six of the eight stars showed no unambiguous variability .
five of the six : he 2 - 141 , ngc 3132 , ngc 4361 , ns 238 , and sp 3 , where observed on at least four nights , with @xmath2 minutes of consecutive observations on at least one of those nights .
k 1 - 1 was observed on three nights with a maximum duration of 64 minutes .
the light curve of ngc 6026 ( figure [ 6026 ] ) shows obvious variability and suggests a well - behaved periodic nature over the four nights on which observations were made .
the periodogram for ngc 6026 showed periodic variability with a strong one day alias , resulting in a preliminary period of 0.263 days .
this period was taken as a starting point for fitting a sine curve of the form @xmath3\ ] ] where @xmath4 is the instrumental magnitude , @xmath5 is the semiamplitude , and @xmath6 is the period ; either @xmath7 or @xmath8 is a fitted parameter . for the photometry we fit for @xmath7 plus
the remaining parameters and set @xmath8 = 0.75 as is appropriate for variation dominated by an irradiation effect .
this produces an ephemeris with minimum light at phase zero : @xmath9 figure [ 6026 ] 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 0.010 magnitude .
the remaining parameters from the sine fitting are @xmath10 mag ( instrumental ) and @xmath11 mag .
as with ngc 6026 , the light curve of ngc 6337 in figure [ 6337 ] shows apparently well - behaved periodic variability .
the periodogram showed periodic variability with a strong one day alias .
the peak with the most power was located at a period of 0.173 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 6026 .
the derived photometric ephemeris for minimum light in ngc 6337 is then @xmath12 figure [ 6337 ] 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 0.016 magnitude .
the remaining parameters from the sine fitting are @xmath13 mag ( instrumental ) and @xmath14 mag .
the short orbital periods allow limits to be placed on several of the binary system parameters . taking the masses of both css to be @xmath15 , typical of cspne
, kepler s 2nd law gives the binary separation as a function of secondary mass .
the small deviation from a sine curve , short orbital periods , and significant reflection effects observed in the two systems suggest that the companions are cool dwarf stars which do not fill , or just fill , their roche lobes .
to find an upper limit for the secondary masses , i will assume that both secondaries are main sequence stars and do not fill their roche lobes .
this condition is met for the two systems , according to their corresponding orbital periods and for @xmath16 , by @xmath17 and @xmath18 .
these correspond to binary separations of @xmath19 and @xmath20 .
a few comments may be made about the binary system inclinations as well .
corradi et al .
( 2000 ) show that the ring - like structure of ngc 6337 is the narrow waist of a nearly pole - on bipolar pn .
the inclination of the pn then must be @xmath21 for the bright inner ring to have no apparent ellipticity .
ngc 6026 does not appear ring - shaped , but as a partial ellipse with a very faint south - east edge .
if this pn is what bond ( 2000 ) refers to as a `` wedding ring '' pn , then the inclination must be intermediate and can be roughly determined from the ellipticity of the observed pn .
the ellipse measures @xmath22 , giving an inclination of @xmath23 .
if the binary mechanism for shaping pne is correct , then the close binary css must have inclinations equal to those of the pne .
finally , previous studies have found the fraction of detectable close binary cspne to be @xmath24 ( bond 2000 ) .
the binary fraction found here 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 .
if the 25% binary fraction persisted , the binary mechanism for pn shaping would be strongly supported , specifically the scenario outlined by soker ( 1997 ) .
i would like to thank bill bagnuolo , doug gies , and bill nelson for their generous support and todd henry and alberto miranda for their assistance with the ctio 0.9 m telescope .
this research was funded by georgia state university .
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 6337 . 
 the variability matches that expected from a binary system in which a hot primary irradiates a cooler secondary star .