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To Be or Not to Be:The Mysteries of Disk Formation
Around Rapidly Spinning Be Stars
Douglas R. GiesDepartment of Physics and Astronomy
Center 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 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, andlinear polarization (of scattered star light)
• Disk features inherently time variable:B → Be → B …(months to decades)
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• Detailed spectra show emission intensity is split into peaks to blue and red of line-center.
o
Intensity
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
“e” = emission lines in the spectrum
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Examples of Temporal Variations:Be stars in cluster NGC 3766
200320052006
McSwain 2006
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Gamma Cas
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134 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 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
• >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. 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
• 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 exponentH(R) = R3/2 Cs / VK = disk scale height
• Observer parametersi = inclination of disk normalα = 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 diskI = Sd (1-e -τ) + S* e -τ
Sd = source function for diskS* = 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 fitα=116º, i=51º, ρ0=7x10-11, n=2.7
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φ Per: binary with P = 126.7 dα=49º, i=69º, ρ0=1x10-11, n=1.8
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ζ Tau: single star fitα=38º, i=90º, ρ0=2x10-10, n=3.1
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κ Dra: binary fit with P = 61.6 dα=21º, i=26º, ρ0=6x10-13, n=0.7
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Sanity Checks: IR Excess
Parameter γ Cas φ Per ζ Tau κ 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: Hα InterferometryParameter γ Cas φ Per ζ Tau κ Dra
α (MkIII) 109 28 32 …
α (NPOI) 121 29 28 …
α (CHARA) 116 49 38 21
i (MkIII) 46 63 >74 …
i (NPOI) 55 >55 >74 …
i (CHARA) 51 69 90 26
θ (MkIII) 3.5 2.7 4.5 …
θ (NPOI) 3.6 2.9 3.1 …
θ (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 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 CasWλ = -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 …