Pulsation, angular momentum transport and loss, and event-driven asteroseismology in rapidly-rotating OB stars
Abstract
Classical Be stars are non-radial pulsating, rapidly-rotating, near main-sequence OB stars that (occasionally) host self-built gaseous decretion disks. While the exact mechanism(s) that lead to disk formation remain unknown, it is evidently related to internal processes that rise to the surface, ultimately resulting in the escape of mass and angular momentum (AM). A deeper understanding of the pulsational properties of these objects likely holds the key to determining how AM is transported throughout the stellar interior and subsequently leaves the star via a disk, thereby avoiding an ‘AM crisis’ which would otherwise destroy the star. Space photometry has been pivotal in revealing the pulsational frequencies in these stars, and in particular those linked to mass ejection events. Since the launch of the TESS mission, we have been monitoring select Be stars with intensive high-cadence optical echelle spectroscopy contemporaneous with TESS observations. Combining these datasets allows for the characterization of: 1) stellar pulsation modes, 2) mass ejection events (and the concurrent changes in pulsation patterns), 3) the initial distribution of ejecta and its evolution (on timescales of hours to days) into a disk, and 4) stellar properties including rotation rate, mass, radius, and inclination angle. We have demonstrated that it is the rule that mass is ejected from some localized region at the stellar equator for discrete events (rather than a symmetric outflow), and that material freely orbits (rather than forced co-rotation). Further, it is now clear that the pulsational properties change drastically during active mass ejection, opening up the possibility of ‘event-driven asteroseismology’ which can complement steady-state asteroseismology.
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Pulsation, angular momentum transport and loss, and event-driven asteroseismology in rapidly-rotating OB stars Fig. 3) The top three panels show an SPH model where a blob of material is initialized and allowed to evolve with viscous and gravitational forces as material orbits the star. The bottom-left panel shows the emergent Hα flux at a few timesteps during the first two days of the simulation. The bottom-right panel shows the observed Hα emission at a few epochs during the first two days of an outburst for the Be star f Car (whose stellar parameters were used for the SPH model). The qualitative agreement is encouraging. The SPH models are being refined to more realistically describe the ejecta initial conditions (e.g. size, density, velocity profile). TESS + spec frequencies - rotation, pulsation, orbit: Besides outbursts, the most conspicuous photometric feature of Be stars is the presence of one to several frequency groups. The stellar rotation frequency is generally located within or near the first group, and the second group is located at about twice the frequency of the first. The rapid V/R frequencies during outburst are also located within this first group, and the dominant spectroscopic pulsation frequency is at the high-frequency edge of the first group. Fig. 4 compares signals from phot + spec. New photometric frequencies that appear during outburst are on the low-frequency side of groups (Fig. 5). Common patterns: - The V/R frequencies are consistent with material orbiting close to the stellar surface, and are faster than the stellar rotation (Fig. 6; consistent with sub-critical rotation, and disfavoring co-rotation) - The dominant spectroscopic pulsation signal is faster than the V/R (and rotational) frequencies, consistent with prograde pulsation - All systems with short outbursts seem to have frequency groups Fig. 4) Frequency spectra (black solid curve) are plotted from TESS data. The periods of the rapid V/R cycles for these stars are indicated by solid red vertical lines, and spectroscopic pulsational frequencies are indicated by dotted blue vertical lines. In all cases, the spectra were taken during TESS observing run. The spectroscopic pulsation frequency has a photometric counter part in all stars except kap CMa. Fig. 6) EWV/EWR frequencies vs. orbital frequencies at different radii. Blue symbols: orbital frequency calculated at a distance of 1.5 Rpole from the star. Red symbols: orbital frequency calculated at Requator. The solid lines show a linear fit to the points and the the green dashed line indicates x=y. Fig. 5) TESS frequency spectrum for the Be star f Car during quiescence (black) and during outburst (orange). The dotted blue lines are spectroscopic pulsation frequencies, and the green lines are in-outburst EWV/EWR frequencies. It is not yet clear what the newly-emergent in-outburst frequencies represent, but are perhaps suddenly-excited short-lived pulsation modes. Classical Be stars: Main sequence B-type stars with circumstellar “decretion” disks Key Ingredients Near-critical rotation. Low equatorial surface gravity Multi-mode non-radial pulsation Mechanical mass ejection (not winds) “Decretion” disk is formed (hot gas, Keplerian, viscosity) ●Rotation rate ●Oblateness ●Surface gravity + Teff ●Gravity darkening ●Waves carry energy + momentum ●Temperature + velocity perturbations ●mode coupling ●Density + temperature + velocity distribution ●Behavior of ejecta ●Circularization timescale Physical parameters ●Transport of mass and angular momentum outward ●Role + strength of viscosity ●Slow oscillations ●Tidal interaction with companion + Timescale Prot ~ 0.5 - 3 d Ppulse ~ 0.1 - 3 d Porb ~ 0.5 - 3 d tdisk ~ 5 d - 100 yr ●Vsini ●polarimetry + interferometry ●asteroseismology Periodic signals in: ●brightness ●line profile shape + RV ●Continuum brightness ●Variable emission features ●Polarimetry ●Continuum brightness ●Emission features ●Polarimetry ●Interferometry Observables Binary mass transfer -> spin-up of eventual Be star + hot stripped He subdwarf ●Initial masses, separation ●M + AM transfer rates ●efficiency of mass transfer ●Binary spin-up common, but not required Porb ~ 5 - 100 d ●binary RVs ●Brightness at Porb ●Emission + phot. var. from accretion + disk A. M. Geller Rivinius+2013 Neiner+2020 Gabriel Pérez - SMM (IAC) CHARA Goal/Aims : TESS photometry + simultaneous high-cadence echelle spectroscopy to study these processes Goal/Aims - TESS photometry + high-cadence echelle spectroscopy to study these processes: - Understand pulsational properties and links to mass ejection - Track evolution of ejecta from initial conditions to symmetric disk - Measure flux of mass and angular momentum out of the system TESS photometry Spectroscopy - emission strength Fig. 1) Two mass ejection events. Brightness + emission increase as circumstellar material accumulates, and fade as material dissipates. Rapid photometric variations are pulsational. Right: H-alpha emission profiles taken at the times indicated by the two triangles in the bottom panel. A disk is formed in just 4 days. Fig. 2) During mass ejection (disk build-up) emission is always localized in velocity (i.e. circumstellar material is localized in azimuth). The asymmetry oscillates, providing the orbital period of the ejecta. The two highlighted spectra on the bottom panels are taken 0.632 days apart, highlighting the rapid asymmetry changes. TESS photometry Emission asymmetry Labadie-Bartz+2025 “The birth of Be star disks - I. From localized ejection to circularization” studied ~35 mass ejection events like in Figs. 1, 2. We conclude: ●100% of events showed emission asymmetry oscillations with a characteristic frequency consistent with a Keplerian orbit near the equator (Fig. 2). ●Material was always launched from a localized region on the stellar surface (Figs 2, 3). ●Ejected material became symmetric (disk-like) after ~5 - 10 orbital timescales (Fig. 2). ●Not forced co-rotation (e.g. from magnetic fields), but rather a ballistic launch (Fig. 3). ●Photometric pulsation signals are usually enhanced during mass ejection (Fig. 1). ●Links between pulsation, rotation, rotation, and orbital frequencies (Fig. 4). ●Pulsation observed in all Be stars (also Labadie-Bartz+2022). ●Work still ongoing. Can we understand how (or if) pulsation drives mass ejection? How close to critical is rotation? How are Keplerian velocities achieved? How is AM transported internally? Fig. 3) SPH model where a blob of material is launched from a region on the star and evolves with gravity and viscosity. The bottom-left panel shows the emergent Hα flux at a few timesteps during the first two days of the simulation. The bottom-right panel shows the observed Hα emission at a few epochs during the first two days of an outburst for the Be star f Car (Fig. 1). Fig. 5) TESS frequency spectrum for the Be star f Car during quiescence (black) and during outburst (orange). The dotted blue lines are spectroscopic pulsation frequencies, and the green lines are in-outburst EWV/EWR frequencies. It is not yet clear what the newly-emergent in-outburst frequencies represent, but are perhaps suddenly-excited short-lived pulsation modes. Stable TESS signals (black) Spec. pulsation frequencies Circumstellar orbital frequencies Transient in-outburst TESS signals Fig. 4) Frequency information from TESS (black for stable signals, orange for emergent signals during mass ejection), spectroscopic line profile variations, and the circumstellar orbital frequencies measured from emission-line oscillations. Jonathan Labadie-Bartz (DTU Space; j[email protected]) …in collaboration with Alex Carciofi, Amanda Rubio, Dietrich Baade, Noel Richardson, Tajan Amorim, Yael Naze, Coralie Neiner, Thomas Rivinius, Catalina Arcos, and many amateur astronomers These SPH models + HDUST radiative transfer qualitatively reproduce: ●TESS photometric signals of mass ejection ●Hydrogen emission line shapes and strength ●Emission line asymmetry cycles ●Circularization timescales ●And more! …but we are out of space. Stay tuned for Rubio et al., in prep. “The birth of Be star disks - II. SPH models of localized mass ejections” Heavily inspired by, and made possible thanks to: Štefl et al. (1995, 1998, 2003), Rivinius et al. (1998, 2001, 2003, 2013), Baade et al. (2016, 2018), Ricker et al. (2015), Rimulo et al. (2018), Neiner et al. (2002, 2005, 2020), Floquet et al. (2000), Zorec et al. (2016), Richardson et al. (2021), Labadie-Bartz et al. (2018, 2022), Carciofi & Bjorkman (2006), Huat et al. (2009), Semaan et al. (2018), and the BeSS database with 200+ observers (mostly amateurs), with special thanks to the validators and administrators: B. de Batz, C. Neiner, E. Alecian, C. Buil, S. Charbonnel, F. Cochard, V. Desnoux, O. Garde, M. Kraus, T. Lemoult #61 +? (this part is still mysterious)