The Rocket Science of Launching Stellar Disks

Stan OwockiUD Bartol Research Institute

Disks in SpaceStan Owocki

Bartol Research InstituteUniversity of Delaware

Where do stars, planets, we, come from??

• From collapse of interstellar gas clouds

• Gravity pulls together

• But clouds usually have small spin

• Amplified on collapse

• Leaves behind disk

• For proto-sun, this collapsed into planets, earth, us

Saturn’s rings

Spiral Galaxies

Disk in Center of Galaxy

Beta Pictoris

Gaseous Pillars in M16

Proto-stellar nebuale

Protostellar Collapse

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Binary mass exchange

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Binary mass exchange

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Gravity

GMmF = _____ r2

Angular mometum

l = m v r~ constantQuickTime™ and a

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Centrifugal force

mv2f = ___ r

Orbital motion

centrifugal force f = mv2/r ~ 1 / r3

gravity F = GMm / r2

v2 = GM/rwhen F=f

Key: Infalling matter must shed its angular momentum

Summary: Disks from Infalling Matter

• Star formation– protostellar disk

– led to planets, Earth, us

• Binary stars– overflow onto companion

– spirals down through disk

The Rocket Science of Launching Stellar Disks

Stan OwockiUD Bartol Research Institute

Spectral lines & Doppler shift

• Motion of atoms shifts frequency by Doppler effect

• Atoms of a gas absorb & emit light at discrete frequencies

Be stars• Hot, bright, & rapidly rotating stars.• Discovered by Father Secchi in 1868• The “e” stands for emission lines in the star’s spectrum

• Detailed spectra show emission intensity is split into peaks to blue and red of line-center.

o

Inte

nsi

ty

Wavelength

• Indicates a disk of gas orbits the star.

• This is from Doppler shift of gas moving toward and away from the observer .

Hydrogenspectrum

HH

The Puzzle of Be Disks

• And most Be stars are not in close binary systems.

• Be stars are too old to still have protostellar disk.

How do Be starsdo this??

• They thus lack outside mass source to fall into disk.

• So disk matter must be launched from star.

Key Puzzle Pieces

• Stellar Wind– Driven by line-scattering of star’s radiation– Rotation can lead to Wind Compressed Disk (WCD) – But still lacks angular momentum for orbit

• Stellar Pulsation– Many Be stars show Non-Radial Pulsation (NRP) with m < l = 1 - 4

• Here examine combination of these.

• Stellar Rotation– Be stars are generally rapid rotators

– Vrot ~ 200-400 km/s < Vorbit ~ 500 km/s

Rotational Broadening of Photospheric Absorption Lines

Wind Compressed Disk Model

Vrot (km/s) = 200 250 300 350 400 450

Hydrodynamical Simulations of Wind Compressed Disks

Note: Assumes purely radial driving of wind

Inner Disk Infall

• WCD material lacks angular momentum for orbit• Either Escapes in Wind or Falls Back onto star• Limits disk density

Problems with WCD Model

• Inhibited by non-radial forces

• Lacks angular momentum for orbit– inner disk infall– outer disk outflow

• Thus, compared to observations:– density too low– azimuthal speed too low– radial speed too high

• Need way to spin-up material into Orbit

rN

Flux

Launching into Earth Orbit

• Requires speed of ~ 18,000 mi/h (5 mi/s).

• Earth’s rotation is ~ 1000 mi/h at equator.

Cannon atop high mountain

V ~ 18,000 mi/h

V ~ 17,000 mi/h

Cannon at equator• Launching eastward from

equator requires only ~ 17,000 km/h.

• 1-(1- 1/18)2 ~ 2/18 => ~10% less Energy

Launching into Be star orbit

• Requires speed of ~ 500 km/sec.

• Be star rotation is often > 250 km/sec at equator.

• Launching with rotation needs < 250 km/sec

• Requires < 1/4 the energy!

• Localized surface ejection self selects orbiting material.

Vrot = 250 km/sec

V=250 km/sec

Line-Profile Variations from

Non-Radial Pulsation

Wavelength (Vrot=1)

Flux

Rotation

Rotation+

NRP

NRP-distorted star (exaggerated)

Line-Profile with:

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l=4, m=2

NRP Mode Beating

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Pulsation & Mass Ejection

• See occasional “outbursts” in circumstellar lines

• Tend to occur most when NRP modes overlap

• Implies NRPs trigger/induce mass ejections

• But pulsation speeds are only ~ 10 km/s.

• What drives material to ~ 250 km/s??

NonRadial Radiative Driving

• Light has momentum.

• Pushes on gas that scatters it.

• Drives outflowing “stellar wind”.

• Pulsations distort surface and brightness.

• Could this drive local gas ejections into orbit??

First try: Localized Equatorial Bright Spots

Symmetric Bright Spot on Rapidly Rotating Be Star

Vrot = 350 km/sVorbit= 500 km/s

Spot Brightness= 10Spot Size = 10 o

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RDOMERadiatively Driven Orbital Mass Ejection

• Assume localized distortion in

surface height & brightness.

• If phase of brightness leads height,

then can get “prograde flux”.

• Can this drive mass into orbit?

Time Evolution of Single Prograde Spot

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Prominence/Filament

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Force Cutoff

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Outward Viscous Diffusion of Ejected Gas

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Time Evolution of m=4 Prograde Spot Model

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Summary

• Disks often form from infall.

• Be disks require high-speed surface launch.

• Like Earth satellites, get boost from rotation.

• Pulsation may trigger gas ejection.

• Driving to orbital speed by light, perhaps from tilted bright spots???

V=250 km/s