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Next: Time-resolved spectra of G 226-29 Up: Modeling time-resolved spectra Previous: Introduction

Time-resolved spectra and non-linear effects

There is more than one aim in our calculations. First, we want to be able to calculate amplitude spectra of oscillations. In Fig. 1 we show for l=1 to l=4 the normalized amplitude spectra (which are independent, for small amplitudes, of the often unknown inclination i; e.g., RKN, BFW). As one can see from Fig. 1, the slope varies strongly with l. By comparing the observed slope with the theoretical slope, one can therefore determine l (the slope also depends on tex2html_wrap_inline230 and tex2html_wrap_inline252 , which may have to be constrained from other observations).

Figure: Normalized amplitude spectra for l=1 (solid), l=2 (dashed), l=3 (dotted) and l=4 (dash-dotted) modes ( tex2html_wrap_inline304 , tex2html_wrap_inline306 , tex2html_wrap_inline200 ). Around 1900 Å the phase of the l=4 mode changes by tex2html_wrap_inline204 , causing the amplitude to go to zero

A second aim of our program is to calculate time-resolved spectra. This is shown in Fig. 2 for l=1, m=0 for a strong oscillation resulting in variations of tex2html_wrap_inline230 of tex2html_wrap_inline320 . One can see that the spectra depend strongly on the inclination. Furthermore, one can see the effects of having a distribution of tex2html_wrap_inline230 at maximum and minimum instead of a uniform tex2html_wrap_inline230 across the WD surface.

Figure 2: UV-spectra at maximum and minimum (solid) for l=1, m=0 oscillations with tex2html_wrap_inline330 for tex2html_wrap_inline212 (left) and tex2html_wrap_inline214 (right). Also shown are the equilibrium spectrum ( tex2html_wrap_inline304 , tex2html_wrap_inline338 , tex2html_wrap_inline200 ; dashed) and spectra at tex2html_wrap_inline342 (dotted)

A third aim is to properly take into account non-linear variations of I with linear, i.e., sinusoidal, variations of tex2html_wrap_inline230 . For the above case we show in Fig. 3 the light curve for a filter located near the center of tex2html_wrap_inline226 and just outside this line. One can see that the light curve differs strongest from the underlying pure sinusoidal variation of tex2html_wrap_inline230 near the center of the spectral line. This causes strong amplitudes at higher harmonics in the Fourier spectrum.

Figure 3: Light curves and corresponding Fourier spectra for oscillations as in Fig. 2 with tex2html_wrap_inline212 close to the center of the tex2html_wrap_inline226 line (left panels) and just outside the tex2html_wrap_inline226 line (right panels). The underlying sinusoidal variation of tex2html_wrap_inline230 is overplotted (dotted)

next up previous
Next: Time-resolved spectra of G 226-29 Up: Modeling time-resolved spectra Previous: Introduction

Horst Vaeth
Thu Sep 26 10:49:14 MET DST 1996