To Be or Not to Be: The Mysteries of Disk Formation Around Rapidly Spinning Be Stars

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To Be or Not to BeThe Mysteries of Disk
Formation Around Rapidly Spinning Be Stars

• Douglas R. Gies
• Department of Physics and AstronomyCenter for
  High Angular Resolution AstronomyGeorgia State
  University

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Outline

• 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 MomentumBe 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, andlinear polarization (of
  scattered star light)
• Disk features inherently time variableB ? Be ?
  B (months to decades)

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e emission lines in the spectrum

• 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.

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Examples of Temporal VariationsBe stars in
cluster NGC 3766
2003
McSwain 2006
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
• StagesBe He star ? f PerseiBe neutron
  star? Be X-ray binaries

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Going to the Extreme BeXRBs

• SN results in neutronstar in elliptical orbit
• Accretion X-ray fluxshould attain max. near
  periastron
• How large can disksgrow in BeXRBs?

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Grundstrom and Astr 8600

• gt3 year survey of three BeXRB systems
• Measured Ha strength in spectra from the KPNO
  Coudé Feed telescope
• Developed code for relationship between Ha
  strength and disk radius (dependent on disk
  temperature and inclinationGrundstrom 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 radiusRd / Rs 4.6(41 resonance)
• Historical max. Rd / Rs 5.6( periastron)
• Photoionization of disk in 1 day?

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HDE 245770 A 053526(P 110 d, e
0.47)(Grundstrom et al. 2007, ApJ, submitted)

• No disk in 1998
• Recent disk radius Rd / Rs 5(51 resonance?)
• Historical max. Rd / 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 radiusRd / 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

• Ha disks observed by Tycner et al.
• Expect IR excess from ionized gas f-f and b-f
  emission
• Should appear in K-band (? 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 (p,
  Rs)
• Disk geometry (Hummel Vrancken 2000)?(R,Z)
  ?0 R-n exp-0.5(Z/H(R))2?0 base density (g
  cm-3)n radial density exponentH(R) R3/2 Cs
  / VK disk scale height
• Observer parametersi inclination of disk
  normala 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 ?2 along rays through
  disk I Sd (1-e -t) S e -tSd source
  function for diskS source function for
  uniform star
• Fourier transform images to get visibility
  V(Aufdenberg et al. 2006)

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? Cas i51º, ?07.2x10-11, n2.7
Minor axis
Major axis
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? Cas i80º, ?07.2x10-11, n2.7
. original model with i51º, ?07.2x10-11,
n2.7
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? Cas i51º, ?03.6x10-11, n2.7
. original model with i51º, ?07.2x10-11,
n2.7
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? Cas i51º, ?07.2x10-11, n2.0
. original model with i51º, ?07.2x10-11,
n2.7
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Fitting the Models

• Search for ?2 minimum for ?0, n, i, a
• All four targets are known binaries, but nature
  of companion unknown for all but the case of f
  Per
• Determined both fits as single Be and as Be plus
  hot subdwarf companion ? inclusion of companion
  significantly improved fits for ? Dra and f Per

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? Cas single star fita116º, i51º, ?07x10-11,
n2.7
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f Per binary with P 126.7 da49º, i69º,
?01x10-11, n1.8
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? Tau single star fita38º, i90º, ?02x10-10,
n3.1
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? Dra binary fit with P 61.6 da21º, i26º,
?06x10-13, n0.7
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Sanity Checks IR Excess
Parameter ? Cas f Per ? Tau ? Dra
E(V-K)(Dougherty et al.) 0.85 0.68 0.65 0.39
E(V-K)(K model) 1.60 0.63 0.53 0.14
Disk densities may have varied over 15 years
between the IR and CHARA Array measurements
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Sanity Checks Ha Interferometry
Parameter ? Cas f Per ? Tau ? Dra
a (MkIII) 109 28 32
a (NPOI) 121 29 28
a (CHARA) 116 49 38 21
i (MkIII) 46 63 gt74
i (NPOI) 55 gt55 gt74
i (CHARA) 51 69 90 26
? (MkIII) 3.5 2.7 4.5
? (NPOI) 3.6 2.9 3.1
? (CHARA) 2.0 2.3 1.8 1.8
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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 Ha
• Total disk mass ranges from 8x10-8 (? Dra) to
  2x10-6 (? 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 ? Cyg
  this past summer
• Yamina Touhami will observe ? 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 Ha strength)

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Upcoming CHARA Program
? CasW? -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 ones sanity to the brink in
  life