Micro-turbulence across the Hertzsprung-Russell diagram. Observational constrains for stars in the MW

TL;DR

This study maps photospheric micro-turbulence across the HR diagram by assembling a homogeneous database of $T_{ m eff}$, $ ext{log g}$, $v\sin i$, $v_{\rm mac}$, and $v_{\rm mic}$ for over 1800 Galactic stars spanning O to K types. Through careful bias control and multiple, consistent analysis techniques, the authors show that $v_{\rm mic}$ is a genuine physical phenomenon, likely linked to envelope convection and possibly pulsations in some stars, with systematic effects on $v\sin i$ and $v_{\rm mac}$ measurements. A key finding is the strong empirical connection between micro-turbulence and turbulent pressure from subsurface convection zones, supporting a convection-driven origin for small-scale surface motions and offering a framework to interpret macroturbulence and the OB mass-discrepancy. The resulting database provides a valuable resource for testing theories of hot-star atmospheres and the role of micro-turbulence in stellar evolution and parameter determination.

Abstract

We assemble a homogeneous database of precise and consistent determinations of effective temperature, surface gravity, projected rotational rate, and macro- and micro-turbulent velocities for over 1800 Galactic stars spanning spectral types O to K and luminosity classes I to V. By carefully minimizing biases due to target selection, data quality, and disparate analysis techniques, we carry out statistical tests and comparative analyses to probe potential dependencies between these parameters and micro-turbulence. Our findings indicate that photospheric micro-turbulence is a genuine physical phenomenon rather than a modelling artifact. A direct comparison between observed micro-turbulent velocities and corresponding theoretical predictions for the turbulent pressure fraction strongly suggests that this phenomenon most likely arises from photospheric motions driven by envelope convection zones, with an additional pulsational component likely operating in main-sequence B stars. We show that neglecting micro-turbulent broadening in Fourier transform analyses can partly explain the dearth of slow rotators and the scarcity of stars with extremely low macro-turbulent velocity. We argue that including micro-turbulent pressure in atmospheric modelling can significantly mitigate (even resolve) the mass discrepancy for less massive O stars. Our database offers a valuable resource for testing and refining theoretical scenarios, particularly those addressing puzzling phenomena in hot massive stars.

Figures (11)

• Figure 1: Distribution of the sample stars by spectral type and luminosity class (LC V/IV -- red; LC III -- light blue; LC II/I -- grey), and by the type of pulsations. Upper panel -- non pulsating stars; lower panel -- sample pulsators. In both cases shaded areas indicate the number of objects with photometric $T_{\rm eff}$ and $\log g$ determinations.
• Figure 2: Spectroscopic HR diagram of the sample stars with data-points colour-coded and size-scaled according to their $v_{\rm mic}$ value, as indicated in the legend. Overplotted are: the brott11 evolutionary tracks for single stars with solar metallicity and initial rotational velocity $V_{\rm rot}$ = 300 km s$^{\rm -1}$ ; the Eddington limit (horizontal dotted line); the observed HD limit (gray solid thick lines) and the temperature boundaries corresponding to each spectral type (red almost vertical lines). Error bars are omitted for clarity. For more information see Sect. \ref{['vmic_shrd']}
• Figure 3: Photospheric micro-turbulence of the sample non-pulsating stars separated by SpT and LC (open circles - LC III/I; solid circles - LC V/IV) as a function of $\log g$ (left) and $T_{\rm eff}$ (right). In the top panels over-plotted are: the $v_{\rm mic}$ velocities of a sample of O stars in the SMC derived by means of the CMFGEN code (from heap06), and the theoretical $T_{\rm eff}$ and $\log g$ scales of O stars in the MW predicted by martins05a(red solid (DWs) and dashed (SGs) vertical lines). In each plot representative error bars are also indicated. For more information, see Sect.\ref{['vmic_spt']}.
• Figure 4: Photospheric micro-turbulence of the sample non-radial pulsators (separated by the type of oscillations), and of the classical Cepheids and Red Giants/Supergiants (symbols highlighted in light/dark blue) as a function of $\log g$ (left) and $T_{\rm eff}$ (right). For the case of non-RPs analogous results for non-pulsating stars of similar $T_{\rm eff}$ , $\log g$ and $\mathcal{L}$/$\mathcal{L}{_\odot}$ (colour coded as indicated in Fig. \ref{['fig3']}), are also provided for a direct comparison. In each panel the horizontal dashed lines indicate the upper/lower limits to $v_{\rm mic}$ İn the left fifth raw panel, the light and dark blue lines represent the mean $v_{\rm mic}$ , averaged within the subgroups of low- and high-mass Cepheids, respectively; in the bottom left panel, the red line indicates the least square fit to $v_{\rm mic}$ of the sample RGs thereby highlighting the deviation of RSGs from this trend. For more information see Appendix \ref{['A']}.
• Figure 5: Photospheric micro-turbulence of the sample stars (pulsating and non-pulsating) as a function of log$\mathcal{L}$/$\mathcal{L}{_\odot}$ (=[$T_{\rm eff}$$^{4}$/$g$]). The data points are color coded according to their SpT (as indicated in the legend) with Slowly Pulsating B-stars (SPBs) highlighted in light blue. Vertical lines divide the sample into four spectral luminosity subgroups, depending on the maximum $v_{\rm mic}$ velocity achieved by the corresponding stars (horizontal dotted lines), with the red one indicating the approximate limit between the high and low mass regimes (for more information see text).