Critical study of the distribution of rotational velocities of Be stars

Abstract

Aims. We assume that stars may undergo surface differential rotation to study its impact on the interpretation of Vsin i and on the observed distribution Φ(u) of ratios of true rotational velocities u = V/V c (V c is the equatorial critical velocity). We discuss some phenomena affecting the formation of spectral lines and their broadening, which can obliterate the information carried by Vsin i concerning the actual stellar rotation. Methods. We studied the line broadening produced by several differential rotational laws, but adopted Maunder's expression Ω(θ) = Ω 0 (1 + α cos 2 θ) as an attempt to account for all of these laws with the lowest possible number of free parameters. We studied the effect of the differential rotation parameter α on the measured Vsin i parameter and on the distribution Φ(u) of ratios u = V/V c . Results. We conclude that the inferred Vsin i is smaller than implied by the actual equatorial linear rotation velocity V eq if the stars rotate with α < 0, but is larger if the stars have α > 0. For a given |α| the deviations of Vsin i are larger when α < 0. If the studied Be stars have on average α < 0, the number of rotators with V eq 0.9V c is larger than expected from the observed distribution Φ(u); if these stars have on average α > 0, this number is lower than expected. We discuss seven phenomena that contribute either to narrow or broaden spectral lines, which blur the information on the rotation carried by Vsin i and, in particular, to decide whether the Be phenomenon mostly rely on the critical rotation. We show that two-dimensional radiation transfer calculations are needed in rapid rotators to diagnose the stellar rotation more reliably.

Study of a sample of faint Be stars in the exofield of CoRoT

“…Among the unexplored phenomena in rapidly rotating B-type stars is the interaction between pulsations and magnetic fields. In addition, the subphotospheric convection zones may undergo differential rotation (Zorec et al 2011(Zorec et al , 2016(Zorec et al , 2017 to induce new characteristics to the pulsation spectra. It must be noted that the current spectropolarimetric observations and numerical simulations rule out the presence of any ordered small-scale fields stronger than some 50-250 G in Be stars Kochukhov & Sudnik 2013).…”

Automatic algorithm to obtain $v \sin i$ values via Fourier Transform in BeSOS database

“…The 4 3 8 7 4 4 7 1 4 7 1 3 4 9 2 1 5 0 1 5 5 0 4 7 5 8 7 5 6 6 7 8 He I lines (A) with the fractional radius of the star, which is dependent on the colatitude for a fast spinning star and gives rise to an oblate geometry (Harrington & Collins 1968). Although sounding reasonable, a detailed examination of the classical von Zeipel's equation results in a problem known as the von Zeipel's paradox (Zorec et al 2017), where stellar layers outside the stellar core present nonzero divergence of the radiative flux that gives rise to meridional circulations known as Eddington-Sweet currents (Tassoul 2007). Further improvements to the theory were proposed (Espinosa Lara & Rieutord 2011;Zorec et al 2017) leading to a different structure of fractional radii and a different dependence of temperatures and radiative fluxes with the stellar colatitude.…”

“…Our FT analysis in this work considers spherical shapes and rigid rotation, neglecting subtle GD and geometrical deformation. It is worth emphasising that previous works revealed that projected rotational velocities measured from the fittings of classical model atmospheres or even FT techniques are indeed apparent quantities if these effects are not considered, leading possibly to 𝑣 sin 𝑖 underestimations (Stoeckley 1968;Townsend et al 2004;Zorec et al 2016Zorec et al , 2017. In order to figure out, to some extent, the difference between classical FT estimations and models accounting for GD, we performed fittings of GD models to the observed stellar spectra using a code to account for the classical von Zeipel's effect (ZPEKTR; Levenhagen 2014; Levenhagen et al 2021).…”

“…For a complete study, non-linear solutions should be taken into account using a grid of limb-darkening coefficients to simulate the rotation profiles of stellar photospheres. Also, effects of gravity darkening need to be included (Frémat et al 2005;Zorec et al 2017) since for fast rotators, the emerging flux from equatorial regions are reduced as the local gravity in these regions are small, which leads to the underestimation of 𝑣 sin 𝑖. We plan to employ the ZPEKTR code (Levenhagen 2014) to include the classical GD effects and also the Espinosa-Lara's scheme (Espinosa Lara & Rieutord 2011) for high rotating stars in further studies.…”

New Oe Stars in LAMOST DR5

“…Details of the formation of the rotating "decretion" (outwardly moving) disks in Oe (and Be) stars remain complex and puzzling (Struve 1931;Zorec et al 2016Zorec et al , 2017Lee et al 1991;Osaki 1986;Rivinius et al 2001). Undoubtedly, a larger Oe sample can help understand the nature of this type of emission-line star.…”