1. Binary Star Analysis with Intrinsic Pulsation
R.E. Wilson1, W. Van Hamme2, & G.J. Peters3
1 Univ. Florida
2 Florida International Univ.
3 Univ. Southern California

2. An Analytic Model (not structural)
Stars actually pulsate – not limited to spheres
Major advantage and driver of model development: eclipse
effects on pulsation amplitude and waveform naturally
arise from the computations
Has capabilities of the more advanced EB light/velocity curve
models, like:
proper datapoint weighting
simultaneous solution of RV and multi-band curves
tidal/rotational star figures
reflection effect
eclipses, etc.
For now – radial pulsation only -- non-radial later?

3. What does the development accomplish?
Enables coherent resolution of a pulsation waveform into
a geometric and a radiative part, impersonally, given
multi-band light curves (color info allows geometric and
radiative behavior to be distinguished)
Allows fitting light curves consistently (no removal of
eclipses, no removal of pulsation, with iteration)
Deals with radial pulsation in non-spherical stars
Math developed for orbital ephemerides, T0, P, dP/dt, applies
as well to pulsation ephemerides (Ap&SS, 296, 197)
-- which enhances dP/dt accuracy (pulsational and orbital)

4. A present simplification:
Pulsation is assumed slow enough to be computed as a sequence
of equilibrium states (no pulsational dynamics – maybe later)
So the idea is just to be reasonably consistent while inferring
geometric and radiative pulsational properties from their
influences on light & RV curves, not being limited to spherical stars

5. How are the computations done ? (Overview)
A multiplicative waveform in mean radius is introduced (the stars
can have tidal and rotational distortions)
-- and another such waveform is introduced in mean Teff
Each waveform is a Fourier series (fundamental and two harmonics so far)
Coherent separation of geometric and radiative behavior is
deduced from observed behavior (Least Squares criterion),
allowing comparisons with structural pulsation computations
Multi-mode pulsators? OK, just need more pulsation parameters
(or successive applications)
All W-D model capabilities are in place such as solution
constraints, 3 kinds of weighting, simultaneous light/RV solutions,
solutions in absolute units, etc.

6. How are the computations done ? (Specifics)
The geometric multiplier (R_wave) is converted to a volume
multiplier at given pulsation phase via
V= R_wave^3
Then V(phase) is converted to potential (phase), and the star’s
figure is computed as an equipotential and its local effective
gravities are computed from the potential gradient, etc.
The process skips over dynamics (but there’s tomorrow)
Then compute light or magnitude or RV in the usual way.
So the procedure does NOT just fit a wave to a light curve
– it operates at a deeper conceptual level

7. Initial Application: V1352 Tau
80+ days of Kepler data; total/annular eclipses; multi-mode
pulsations; P_orb=6.9 days; P_puls=0.09 days (analyzed)

9. Mean Temperature Variation Only (no geometric variation)

10. Geometric Variation Only (no pulsational Temperature Variation)

11. Geometric and Temperature Variation Together

12. Direct Comparison of Geometric and Temperature Related Waveforms
(Dashed is for temperature)

13. Misc. Variations in the context of EB Variation

14. Results from a Differential Corrections Solution for V1352 Tau
Incl / deg.
T K
T / K
Ref. time (orb.) / d.
P orb / d.
m2/m /
Ref. time (puls) / d.
P puls / d.
dP/dt puls nil
L1/(L1+L2) /
third light /

15. Variations other than 0.09 day pulsation and binary-related