Effect of fluctuations in Doppler width on the center of strong absorption lines

Stochastic temperatures and turbulence are characterized by average velocities u _th and < u _turb  > ≡ u ₀ and fluctuations ${u'_{th}}$ and u′ (<u′ > = 0). Thus, the Doppler width of a line also has a fluctuating component $\Delta {\lambda '_D}$. Observed spectra correspond to the radiative flux averaged over time and over a star’s surface, <H_λ>. Usually, only the average velocities u _th and u ₀ are taken into account in photospheric models and these yield the Doppler width $\Delta \lambda_D^{(0)}$ of a line in the customary way. The fluctuations $\Delta {\lambda '_D}$ mean that near a line center the average absorption coefficient < α_λ > is larger than the usual α_λ, which depends only on the average velocities u _th and u ₀. This enhances the absorption line near the center and is not explained by the photospheric models. This new statistical effect depends on the wavelength of the line. A comparison of observed lines with model profiles yields an estimate for the average level of fluctuations in the Doppler width, $\eta = {{{\left\langle {\left| {\Delta {{\lambda '}_D}} \right|} \right\rangle }} \left/ {{\Delta \lambda_D^{(0)}}} \right.}$, which characterizes the average stochasticity of a photosphere and is important for understanding the physics of photospheres. The depths of lines in synthetic spectra of stars are often greater than the observed values. The observed disagreement between the theoretical and actually observed depths of lines can be corrected by introducing an additional parameter, the fluctuation level η. Then it is possible to obtain estimates of η for a number of stars.