A Pulsational Mechanism for Producing Keplerian Disks around Rapidly Rotating Stars Steven R. Cranmer Harvard-Smithsonian CfA

Emission-line B stars (Be stars) “Classical” Be stars are non-supergiant B stars that exhibit (or have exhibited in the past) emission in H Balmer lines. A wide range of observed properties is consistent with Be stars having dense equatorial disks & variable polar winds. Be stars are rapid rotators, but are not rotating at “critical” / “breakup” Vrot  (0.5 to 0.9) Vcrit (Struve 1931; Slettebak 1988) Unanswered questions: What is their evolutionary state? Are their {masses, Teff, abundances, winds} different from normal B stars? How does the star feed mass & angular momentum into its “decretion disk?”

Movie courtesy John Telting Nonradial pulsations Photometry &spectroscopy reveal that many (all?) Be stars undergo nonradial pulsations (NRPs). Rivinius et al. (1998, 2001) found correlations between emission-line “outbursts” and constructive interference (“beating”) between multiple NRP periods. Observed velocity amplitudes in photosphere often reach 10–20 km/s, i.e., δv ≈ sound speed! Most of the pulsational energy is trapped below the surface, and evanescently damped in the atmosphere. But can some of the energy “leak” out as propagating waves? Movie courtesy John Telting

The acoustic cutoff resonance Evanescent NRP mode: a “piston” with frequency < acoustic cutoff. Bird (1964) Fleck & Schmitz (1991) showed how easy it is for a stratified atmosphere to be excited in modes with ω = ωac . Effects that can lead to “ringing” at ωac : Reflection at gradients in bkgd ? NRP modes with finite lifetimes ? These resonant waves can transport energy and momentum upwards, and they may steepen into shocks.

A model based on “wave pressure” Propagating & dissipating waves exert a ponderomotive wave pressure on a fluid. Cranmer (2009, ApJ, 701, 396) modeled the production of resonant waves from evanescent NRP modes, and followed their evolution up from the photosphere: TΔS depends on shock Mach #, which depends on radial velocity amplitude <δvr2>

Model results for an example B2 V star

Conclusions It seems likely that NRPs can give rise to sufficient angular momentum transport to “spin up disks” around Be stars. Phase changes (Be ↔ Bn ↔ “shell star”) may arise from NRP mode decay/growth, beating, or intermittency from subsurface convection. Testing the full set of proposed processes will require high-resolution simulations which must include radiation forces and extend above & below the photosphere. (Interested? Email: scranmer@cfa !) Understanding has been aided by ongoing collaborations between astrophysics, solar physics, & plasma physics communities.

Extra slides . . .

Observed B-star NRP modes Filled symbols: assumes non-rotating stellar properties Open symbols: attempts to take account of rapid rotation Solid curves: acoustic-gravity propagation boundaries Dotted: f-mode curve

Hot star winds: pulsations & waves Cranmer (1996, 2007) showed that low-frequency modes that are evanescent in the photosphere can leak out into a CAK-type stellar wind. Propagating waves can exert a net “wave pressure” on the wind to provide extra acceleration, and thus a higher mass loss rate! (Neilson & Lester 2008). If pulsations are strong enough, shocks form in the outer atmosphere and push shells out into the wind; see BW Vul (Massa 1994; Owocki & Cranmer 2002).

Rapid rotation Because of competition between gravity and centrifugal forces at the equator, rapid rotators become oblate and “gravity darkened” (von Zeipel 1924). Existence of gravity darkening has been ~confirmed via eclipsing binaries and visible interferometry of oblate stars. For hot stars with radiative interiors, β ≈ 0.25 (down to late-A / early-F) For cooler stars with convective layers below photosphere, β ≈ 0 to 0.08

Rapid rotation: impact on mass loss (Cranmer 1996)

Rapid rotation: impact on mass loss (Dwarkadas & Owocki 2002)