Transcript To Be or Not to Be: The Mysteries of Disk Formation Around

To Be or Not to Be:
The Mysteries of Disk Formation
Around Rapidly Spinning Be Stars
Douglas R. Gies
Department of Physics and Astronomy
Center for High Angular Resolution Astronomy
Georgia State University
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Outline
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Introduction to the Be Stars
Evolution of Interacting Binaries
Be X-ray Binaries (Be + Neutron Star)
CHARA Array Observations of Be Stars
Ongoing and Future Work
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Acknowledgements
• Current Students: Erika Grundstrom,
Tabetha Boyajian, Steve Williams,
Yamina Touhami, Noel Richardson,
Ellyn Baines, Chris Farrington, Astr 8600
• Past students: Ginny McSwain, Wenjin
Huang, Reed Riddle, Dave Berger
• Colleagues: Hal McAlister, Theo ten
Brummelaar, Bill Bagnuolo, David Wingert,
Karen and Jon Bjorkman (Univ. Toledo)
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Accretion and Angular Momentum
• Angular momentum = r x v
• In many gas accretion situations where r
decreases with time, we find that the
momentum ends up in a disk …
• Sun and planets: most of the mass in the
Sun, but most of the angular momentum in
the planets and Oort cloud
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Disks around
proto-stars
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Disks around
black holes
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Disks around
galactic nuclei
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Too Much Angular Momentum:
Be stars (massive stars with disks)
• B spectral type stars (11 – 30 kK) that are
relatively unevolved (core H-burning)
• Circumstellar gas disks revealed by
emission lines (hydrogen Balmer series),
infrared excess continuum emission, and
linear polarization (of scattered star light)
• Disk features inherently time variable:
B → Be → B …(months to decades)
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“e” = emission lines in the spectrum
Hb
Ha
• Detailed spectra show
emission intensity is
split into peaks to blue
and red of line-center.
• This is from Doppler
shift of gas moving
toward and away from
the observer.
• Indicates a disk of gas orbits the star.
Intensity
Hydrogen
spectrum
lo
Wavelength
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Examples of Temporal Variations:
Be stars in cluster NGC 3766
McSwain 2006
2003
2005
2006
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Gamma Cas
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4 of 7 Sisters in Pleiades are Be stars
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Be Stars are Rapid Rotators
Spectral lines are
broadened by
rotation and the
Doppler effect
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How Close to Critical Rotation?
• Spectroscopy suggests Be stars rotate at
≈80% of critical rate (where centripetal
acceleration = gravity at the equator)
• Townsend et al. (2004) show that gravity
darkening will lead to an underestimate of
the rotation rate → 100% critical?
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Temporal Variations:
need rotation plus variable process
Nonradial Pulsation
Magnetic Fields
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Putting the Spin on Be Stars
Why are Be stars rotating so quickly?
• born with high angular momentum
• experiencing a re-distribution of internal angular
momentum near the conclusion of core
hydrogen burning
• received mass and angular momentum through
mass transfer from a binary companion (this
must occur since spin-up observed in Algols
and results of accretion seen in BeXRBs)
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McSwain & Gies (2005)
• Be stars are
neither
very old nor
very young
• Consistent
with idea
that many
form in
binaries
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Evolution of Interacting Binaries
• Many B-stars are
members of close
binary systems
• Stages:
Be + He star
→ φ Persei
Be + neutron star
→ Be X-ray binaries
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Going to the Extreme: BeXRBs
• SN results in neutron
star in elliptical orbit
• Accretion X-ray flux
should attain max.
near periastron
• How large can disks
grow in BeXRBs?
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Grundstrom and Astr 8600
• >3 year survey of three BeXRB systems
• Measured Hα strength in spectra from the
KPNO Coudé Feed telescope
• Developed code for relationship between Hα
strength and disk radius (dependent
on disk temperature and inclination;
Grundstrom & Gies 2006, ApJ, 651, L53)
• Documented disk radius and X-ray flux variations
using NASA RXTE/All Sky Monitor instrument
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LS I +61 303 (P = 26.5 d, e = 0.55)
(Grundstrom et al. 2007, ApJ, in press; astro-ph/0610608)
• Be star + collapsed star with relativistic
jets, gamma ray emission (microquasar)
• Orbit: e = 0.55
• Mean disk radius
Rd / Rs ≈ 4.6
(≈4:1 resonance)
• Historical max.
Rd / Rs ≈ 5.6
(≈ periastron)
• Photoionization of disk in 1 day?
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HDE 245770 = A 0535+26
(P = 110 d, e = 0.47)
(Grundstrom et al. 2007, ApJ, submitted)
• No disk in 1998
• Recent disk radius
Rd / Rs ≈ 5
(≈5:1 resonance?)
• Historical max.
R d / Rs ≈ 9
(≈ periastron)
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X Persei (P = 250 d, e = 0.11)
(Grundstrom et al. 2007, ApJ, submitted)
• Disk growth to
record strength
• Current disk radius
Rd / Rs ≈ 6.4
• But component
separation is large
(Roche radius at
periastron = 34 Rs)
→ how does gas
cross the gap to NS?
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Feeding the X-ray Source
• All three show that
X-ray max. occurs
P/4 after periastron
• Suggests disk
becomes extended
by tidal forces at
periastron
LS I +61 303
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Okazaki et al. (2002)
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I Can See Clearly Now:
Direct Resolution with the CHARA Array
• Hα disks observed
by Tycner et al.
• Expect IR excess
from ionized gas
f-f and b-f emission
• Should appear in
K-band (λ = 2.1μm)
Waters et al. (1991)
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CHARA Array Observations
(Gies et al. 2007, ApJ, 654, Jan. 1; astro-ph/0609501)
• K-band interferometric observations of four
classical Be stars (2003 – 2005)
• Moderate to long baselines
• CHARA Classic beam combiner
• Observations interposed with calibrator
stars with known angular diameter in order
to transform instrumental fringe visibility
into absolute visibility V
• V = Fourier transform of angular image
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Models of K-band Visibility
• Uniform disk star with set angular diameter (π,
Rs)
• Disk geometry (Hummel & Vrancken 2000)
ρ(R,Z) = ρ0 R-n exp[-0.5(Z/H(R))2]
ρ0 = base density (g cm-3)
n = radial density exponent
H(R) = R3/2 Cs / VK = disk scale height
• Observer parameters
i = inclination of disk normal
α = position angle (E from N) of disk normal
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Models of K-band Visibility
• Isothermal disk
Td = 0.6 Teff (star) (Carciofi & Bjorkman 2006)
maximum emission: Planck function for Td
• IR free-free and bound-free optical depth
(Waters 1986; Dougherty et al. 1994)
• IDL code: integrates ρ2 along rays through disk
I = Sd (1-e -τ) + S* e -τ
Sd = source function for disk
S* = source function for uniform star
• Fourier transform images to get visibility V
(Aufdenberg et al. 2006)
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γ Cas: i=51º, ρ0=7.2x10-11, n=2.7
Minor axis
Major axis
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γ Cas: i=80º, ρ0=7.2x10-11, n=2.7
…. = original model with
i=51º, ρ0=7.2x10-11, n=2.7
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γ Cas: i=51º, ρ0=3.6x10-11, n=2.7
…. = original model with
i=51º, ρ0=7.2x10-11, n=2.7
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γ Cas: i=51º, ρ0=7.2x10-11, n=2.0
…. = original model with
i=51º, ρ0=7.2x10-11, n=2.7
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Fitting the Models
• Search for χ2 minimum for ρ0, n, i, α
• All four targets are known binaries, but
nature of companion unknown for all but
the case of φ Per
• Determined both fits as single Be and as
Be plus hot subdwarf companion
→ inclusion of companion significantly
improved fits for κ Dra and φ Per
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γ Cas: single star fit
α=116º, i=51º, ρ0=7x10-11, n=2.7
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φ Per: binary with P = 126.7 d
α=49º, i=69º, ρ0=1x10-11, n=1.8
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ζ Tau: single star fit
α=38º, i=90º, ρ0=2x10-10, n=3.1
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κ Dra: binary fit with P = 61.6 d
α=21º, i=26º, ρ0=6x10-13, n=0.7
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Sanity Checks: IR Excess
Parameter
E(V-K)
γ Cas
φ Per
ζ Tau
κ Dra
0.85
0.68
0.65
0.39
1.60
0.63
0.53
0.14
(Dougherty et al.)
E(V-K)
(K model)
Disk densities may have varied over ≈ 15 years
between the IR and CHARA Array measurements
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Sanity Checks: Hα Interferometry
Parameter
α (MkIII)
α (NPOI)
γ Cas
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121
φ Per
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ζ Tau
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α (CHARA)
i (MkIII)
i (NPOI)
i (CHARA)
θ (MkIII)
θ (NPOI)
θ (CHARA)
116
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55
51
3.5
3.6
2.0
49
63
>55
69
2.7
2.9
2.3
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>74
>74
90
4.5
3.1
1.8
κ Dra
…
…
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…
…
26
…
…
1.8 44
Summary
• BeXRBs: ideal setting to follow disk growth
and accretion fueled X-ray variations
• Nearby Be disks can be resolved with the
CHARA Array
• Disks are smaller in K-band than in Hα
• Total disk mass ranges from 8x10-8 (κ Dra)
to 2x10-6 (γ Cas) solar masses
• Disk filling time ≈ 1 year (BeXRBs)
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Summary
• If we assume (1) mass loss occurs at the
stellar equator and (2) disk gas never
returns, then we can estimate the rate of
angular momentum transferred into the disk:
dJ/dt = -dM/dt Veq Rs
• Time scale for spin down is J / dJ/dt
≈ ¼ main sequence lifetime
• This suggests that disk formation is the
solution of the angular momentum problem
for Be stars
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A Future So Bright:
Work Underway
• Grundstrom dissertation: KPNO Coude
Feed Telescope survey of ≈ 130 Be stars
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Be Spectral Energy Distribution
• NASA IRTF: Flux excess in K, L bands
to constrain Fdisk / Fstar in models for
CHARA Array interferometry
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Upcoming CHARA Program
• Ellyn Baines observed Be stars 59 Cyg and
υ Cyg this past summer
• Yamina Touhami will observe γ Cas next week
with FLUOR (better S/N and bigger disk)
• Yamina will use CHARA Classic in the following
week for a quick survey of Be stars just
observed from KPNO Coude Feed: six targets
should have K-band disk diameters larger than
1.7 mas FWHM (based upon Hα strength)
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Upcoming CHARA Program
ο Cas
Wλ = -32 Å
Predicted K-band
diameter is
3.7 mas FWHM
→ largest yet
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Long Range Plans with CHARA
• Structure in Be disks –
spiral arms
• Time evolution of disks –
follow expansion and dissipation
• Find elusive companions –
source of Be spin
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Hamlet's Soliloquy Revised
(or what if Hamlet had taken up astrophysics)
• HAMLET:
To be, or not to be that is the question:
• GIES:
To Be, or not to Be that is the question:
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Hamlet's Soliloquy Revised
(with apologies to Shakespeare)
• HAMLET:
Whether 'tis nobler in
the mind to suffer
• GIES:
Whether disks overflow
in time and suffer
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Hamlet's Soliloquy Revised
(with apologies to Shakespeare)
• HAMLET:
The slings and arrows
of outrageous fortune
• GIES:
The peaks and troughs
of outrageous pulsation
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Hamlet's Soliloquy Revised
(with apologies to Shakespeare)
• HAMLET:
Or to take arms against
a sea of troubles
• GIES:
Or to make harm against
a B [field] of troubles
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Hamlet's Soliloquy Revised
(with apologies to Shakespeare)
• HAMLET:
And by opposing end them.
To die, to sleep • GIES:
And by ejection end them.
To try, to keep -
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Hamlet's Soliloquy Revised
(with apologies to Shakespeare)
• HAMLET:
No more - and by a sleep
to say we end
• GIES:
fringes galore - and by
good scans today we end
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Hamlet's Soliloquy Revised
(with apologies to Shakespeare)
• HAMLET:
The heartache, and the
thousand natural shocks
• GIES:
The heartache, and the
thousand perverse
knocks
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Hamlet's Soliloquy Revised
(with apologies to Shakespeare)
• HAMLET:
That flesh is heir to.
'Tis a consummation
• GIES:
That interferometry
is heir to.
'Tis an observation
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Hamlet's Soliloquy Revised
(with apologies to Shakespeare)
• HAMLET:
Devoutly to be wished.
To die, to sleep • GIES:
Devoutly to be wished.
To try, to keep -
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Hamlet's Soliloquy Revised
(with apologies to Shakespeare)
• HAMLET:
To sleep - perchance to dream:
ay, there's the rub,
• GIES:
To model - develop
a scheme;
ay, there's the rub,
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Hamlet's Soliloquy Revised
(with apologies to Shakespeare)
• HAMLET:
For in that sleep of death
what dreams may come
• GIES:
For in that chi-squared fit
what bugs may come
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Hamlet's Soliloquy Revised
(with apologies to Shakespeare)
• HAMLET:
When we have shuffled
off this mortal coil,
• GIES:
When data reduction
takes its mortal toil
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Hamlet's Soliloquy Revised
(with apologies to Shakespeare)
• HAMLET:
Must give us pause.
There's the respect
• GIES:
Must give us pause.
There's the aspect
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Hamlet's Soliloquy Revised
(with apologies to Shakespeare)
• HAMLET:
That makes calamity
of so long life …
• GIES:
That takes one’s sanity
to the brink in life …
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