Turbulent velocity variation

The third and the smallest peak of the observed FWHM curve, seen at $\varphi=0.7$, as shows the analysis, is entirely due to the increase of the microturbulence.

  

Figure: Predicted turbulent velocity variation with phase, deduced from the FWHM theoretical fit

With v_turb=0, the theoretical FWHM curve shows only a weak bump two times smaller than observed. Figure shows the predicted variations of v_turb deduced from the FWHM of the FeII line (Fig.). Keeping in mind the notes made above, in the phase region 0.95-1.1 we reconstructed the v_turb curve in a semi-quantitative manner (dashed line).

The reason for a sharp peak at $\varphi=0.94$ is just the numerical result mentionned above that without sharp turbulence amplification at this phase the theoretical minimum of FWHM is too low with respect to observed one. This turbulence peak is probably related to the amplification caused by shock s2, present in our model. If, however, the shock s2 in not present in the real star, the theoretical v_turb peak may probably be the result of underestimation of FWHM due to certain nonadequacy of the description of this very fast phase of model pulsation. Further more sophisticated modelling is then required to clarify this question.

As seen from the figure, v_turb rapidly grows between $\varphi=0.6$ and 0.7 up to about 7km/s from its ``basic'' level of about 2km/s. After that it decreases slowly until $\varphi=0.9$ , almost linearly with phase. A comparison with the density diagram (Fig. ) shows that the origin for this turbulence amplification is most probably the density increase due to another early shock (s3' in Fokin & Gillet, 1997), which pass through the LFR from phase about 0.6 until 0.8. It is rapid enough to provoke by $\varphi=0.7$ the maximum compression in all the line formation region. As a result, at this phase the predicted v_turb reaches its maximum of about 7 km/s (Fig.) , for the observed FWHM is a result of integration of the flux over the whole LFR.

A characteristic feature of RR Lyrae atmospheres is that at the compression phase, the deeper layers are more accelerated by gravity than the upper ones due to considerable extention of the atmosphere. As a result, the density in the atmosphere generally $\it decreases$ during the global compression phase, as can be seen from Fig.. This explain the decrease of v_turb after its maximum at $\varphi=0.7$.