Download - 1 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

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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.

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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

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


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γ Cas: i=51º, ρ0=7.2x10-11, n=2.0


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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: The slings and arrows of outrageous fortune

• GIES: The peaks and troughs of outrageous pulsation

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• 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: And by opposing end them. To die, to sleep -

• GIES: And by ejection end them. To try, to keep -

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• 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: The heartache, and the thousand natural shocks

• GIES: The heartache, and the thousand perverse knocks

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• HAMLET: That flesh is heir to. 'Tis a consummation

• GIES: That interferometry is heir to. 'Tis an observation

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• HAMLET: Devoutly to be wished. To die, to sleep -

• GIES: Devoutly to be wished. To try, to keep -

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• 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: 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: When we have shuffled off this mortal coil,

• GIES: When data reduction takes its mortal toil

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• HAMLET: Must give us pause. There's the respect

• GIES: Must give us pause. There's the aspect

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• HAMLET: That makes calamity of so long life …

• GIES: That takes one’s sanity to the brink in life …

Download - 1 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

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