3. Implementation

A computer program, RAMONE, was written to carry out the modelling described in the previous section. An individual model is calculated for a particular viewing angle , where is the angle between the stellar line of centres and the observer's line of sight, defined such that corresponds to an observer looking along the line of centres through the OVI source to the giant star, while at the source is occulted by the giant star.

3.1. The program flow

The program follows a simple loop structure for each photon packet:

• The initial photon position and direction are calculated.
• If the photon direction is towards the stellar photosphere the optical depth to the next scattering event is found. If this depth exceeds the scattering depth to the photosphere then the photospheric scattering routine is called; otherwise the photon is scattered in the wind. If the photon direction is away from the stellar disk, then the scattering optical depth to the boundary is found and the photon is forced to scatter before the boundary.
• The nature of the scattering event is determined randomly. The probability of a Raman scattering is given by
  
  so if then the scattering is a Raman scattering; otherwise it is a Rayleigh scattering.
• If the photon packet is Rayleigh scattered, then its new direction and polarization are obtained from the Rayleigh-scattering phase matrix, its new frequency is determined in the observer's rest frame, and the loop returns to step (ii). If the photon packet is Raman scattered, then it is scattered towards to the observer. If the cool-star disk intervenes then the packet is absorbed; otherwise it is weighted according to the Rayleigh phase matrix and the absorption optical depth to the observer. The packet goes into the accumulating binned output according to its calculated frequency.

Most of the results we present here are based on Monte-Carlo simulations of the Å line, with input photon packets and errors based on statistics.

3.2. Tests

Many tests were performed on RAMONE. Since the model is circularly symmetric with respect to the observer for models with and , the expected polarization for such models is zero. High signal-to-noise models were run to ensure that the code produced this result, and that the nett value of U was zero.

For models with no absorptive opacity, the fraction of photon packets converted to Raman photons after n or fewer scatterings is

Thus for (1032 Å) or 0.3 (1038 Å) half the Raman scatterings are preceded by 2 or fewer Rayleigh scatterings. Several models were run to confirm that the code's output was consistent with this.

A grid of models was calculated in order to compare the results of RAMONE with those given by Schmid (1992). The Schmid models have no stellar wind, and RAMONE models were run with a negligible mass-loss rate in order to simulate this. Other parameters were adjusted appropriately. A comparison of the line polarizations is shown in Table 1 (click here). The qualitative parameter sensitivity of the line polarization is identical for the two models, but RAMONE gives consistently lower Raman-line polarizations, with values approximately 80% of the Schmid results. Thus the quantitative agreement between the two sets of results is disappointing considering that, in this case, RAMONE was set up to embody essentially identical scattering physics. We have not been able to find a cause for this discrepancy.

  
Table 1: A comparison between Raman-line polarizations obtained by Schmid (1992; S92) and those obtained in this study (RMN).

More-general tests are difficult to construct; however, many of the numerical results reported in the following sections are in qualitative agreement with the expected behaviour of the models.