We propose to test a new method for identifying the spherical harmonic index of pulsation modes in variable white dwarfs, pre-white dwarfs, and central stars of planetary nebulae. Once the mode-indices are found for such stars, the observed periods can yield accurate measurements of mass, luminosity, rotation rate, magnetic field strength, and interior structure. Unfortunately, so far only a single star, PG1159-035, shows a pulsation spectrum rich enough for unambiguous identification of both l=1 and l=2 modes via its observed pattern of periods alone. Theory predicts that limb darkening should cause the amplitudes of l=1 and 2 modes to vary differently with wavelength in the UV. However, previous UV observations directed at determining mode indices in white dwarfs show that the models must be calibrated before this method can prove truly useful. We therefore propose to measure amplitude versus wavelength for the 20 known l=1 and 9 known l=2 modes in PG1159-035 by combining optical data from a WET campaign with time-series UV spectroscopy from the Hubble Space Telescope (STIS FUV-MAMA). Twenty orbits of HST time have already been awarded to this program, with observations currently scheduled for May 9-15, 2002. We will thus measure the limb-darkening law for pre-white dwarfs, calibrate models for future application to other post-AGB pulsators, and truly test a new observational tool of enormous potential.
Within the last few years, a new method of mode identification has been tried with the DA and DB white dwarfs which relies on the fact that, as with the PNe central stars and pre-white dwarfs, the luminosity variations are almost entirely due to temperature (rather than radius) fluctuations (Robinson, Kepler, & Nather 1982). The pulsations divide the stellar surface into zones of higher and lower effective temperature; modes of higher l have more zones than those of lower l. From a distance, we can measure only the integrated surface luminosity, so modes of higher l are washed out by the cancelation of different zones. At ultraviolet wavelengths, the effects of limb darkening increase, decreasing the contribution of zones near the limb to the total luminosity variations. Consequently, modes of higher l are cancelled less effectively in the UV and their amplitudes increase more steeply at short wavelengths than those of low l.
Initially, this technique was only attempted for the DA and DB white dwarfs, because the LTE atmosphere models used to determine limb-darkening effects for these stars were deemed trustworthy, so that observational "calibration" of the technique for modes of different l was thought unnecessary. However, the results have been generally ambiguous (Nitta, Kanaan, & Kepler 2000; Kepler, Robinson, & Koester 2000; and Clemens et al. 2001). Now for the first time, attempts are underway to calibrate this technique using variable stars with well-understood pulsation spectra. One program is studying the variable DB white dwarf GD 358, which has several known l=1 modes, and several suspected l=2 modes (HST GO 8254). Our project attempts to do the same for PG1159-035, which remains the only pulsator among pre-white dwarfs, white dwarfs, or PNe central stars with confirmed modes of both l=1 and l=2.
We propose to observe PG 1159-035 simultaneously with both the WET and HST, to determine the amplitude as a function of wavelength for the 20 known l=1 modes and 9 known l=2 modes of PG 1159-035 (see Winget et al. 1991, for a list of mode-identifications). These modes range in period from 200 to 900 seconds, with typical amplitudes near 1%. Twenty orbits of HST time have already been approved for this program (HST GO 9159). WET coverage will provide the necessary optical wavelength baseline to maximize our ability to differentiate modes of different l. As a result, we will map out the limb-darkening law as a function of wavelength, providing information of unprecedented detail with which to calibrate NLTE atmosphere models for pre-white dwarfs and PNe central stars. Once proven and calibrated, this technique can be applied to identify l values in other stars, which will in turn allow asteroseismological measurement of mass, luminosity, structure, and distance for the majority of variable PNe central stars.
The lightcurve of PG1159-035 is well-studied but also very complex. Previous WET runs have demonstrated the necessity of multi-site observations in measuring the amplitudes of its many pulsation modes. Since white dwarf and pre-white dwarf pulsators commonly change mode amplitudes unpredictably and on very short timescales, we must determine the precise optical amplitudes for as many pulsation modes as possible at the same time as the HST observations. We thus once more require WET observations to help us decode this endlessly fascinating and tremendously useful star.
Justification in LaTEX format
Justification in Postscript format