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Fundamental (Sub)stellar Parameters: Surface

PHY 688, Lecture 11 Outline

• Review of previous lecture – binary and brown dwarfs – (sub)stellar dynamical masses and radii • Surface gravity – stars, brown dwarfs, and giant – determining model-dependent masses • Curve of growth for absorption lines – determining photospheric abundances

Feb 18, 2009 PHY 688, Lecture 11 2 Previously in PHY 688…

Feb 18, 2009 PHY 688, Lecture 11 3 Mass

• most fundamental of stellar parameters – L ∝ M3.8

– τMS ≈ 10 –2.8 10 yr (M/MSun)

• impossible to measure for isolated stars

Feb 18, 2009 PHY 688, Lecture 11 4 Dynamical Masses: Binary Stars to the Rescue • Resolved visual binaries: see stars separately, measure orbital axes and speeds directly. • Astrometric binaries: only brighter member seen, with periodic wobble in the track of its proper motion. • Spectroscopic binaries: unresolved (relatively close) binaries told apart by periodically oscillating Doppler shifts in spectral lines. Periods = days to years. – Eclipsing binaries: seen nearly edge on, so that the stars actually eclipse one another. (Most useful.)

Feb 18, 2009 PHY 688, Lecture 11 5 Visual Binary: GJ 569Bab

• first with a dynamical mass

• measure: P, a, i

(+ a1, a2 if independent astrometric reference exists)

• determine: Mtot

(+ M1, M2)

• a > 5–10AU Feb 18, 2009 (LanePHY 68 8et, L al.ectu 2001)re 11 6 Astrometric Binary: GJ 802AB

• unseen com-panion; first and only to be discovered astrometrically

• measure: P, a1, i (using independent astrometric reference)

• determine: M1

(a2, M2 can be constrained from resolved imaging) (Pravdo et al. 2005)

Feb 18, 2009 PHY 688, Lecture 11 • a > 0.5–2AU 7 Spectroscopic Binary (a) • double-lined (SB2) – spectra of both stars visible (b) (d) (b) (a) (c) (c)

(d) (d) • single-lined (SB1) – only spectrum of brighter visible Feb 18, 2009 PHY 688, Lecture 11 8 Radial Velocity vs. Time for an SB2 in a Circular

• measure: P, v1, v2 • determine: a1 sin i, a2 sin i, M1 sin i, M2 sin i Feb 18, 2009 PHY 688, Lecture 11 9 SB1 Spectroscopic Binary: 51 Peg Ab

• first detected around a main- sequence star – primary SpT: G2 V

• Mp sin i = 0.47 MJup

• 0 AU < a < 10 AU

(Mayor & Queloz 1995) • measure: P, v1 • determine: a sin i, M2 sin i (if M1 approximately known) Feb 18, 2009 PHY 688, Lecture 11 10 Totally Eclipsing Binaries (Are Also SB1’s or SB2’s)

ta – start of secondary ingress tb – end of secondary ingress tc – start of secondary egress td – end of secondary egress

• measure: P, v1, i, ∆F1, ∆F2 (+ v2 if SB2) • determine: a, M1, M2, R1, R2, ratio Teff,1/Teff,2 Feb 18, –200M9 1, M2 determined exactlyP iHf YS 6B882, ;L oectthureer 1w1 ise, only ratio is known 11 First Determination of Substellar Radii: 2MASS 0535–0546 A/B

Feb 18, 2009 PHY 688, Lecture 11 (Stassun et al., 2005) 12 Luminosity-Mass Relation for Stars with Well-determined Orbits

similar relations for radius and

Teff dependence on mass

(Popper 1980) Feb 18, 2009 PHY 688, Lecture 11 13 Outline

• Review of previous lecture – binary stars and brown dwarfs – (sub)stellar dynamical masses and radii • Surface gravity – stars, brown dwarfs, and giant planets – determining model-dependent masses • Curve of growth for absorption lines – determining photospheric abundances

Feb 18, 2009 PHY 688, Lecture 11 14 Given Masses and Radii, Estimate , Surface

•

33 MSun = 2.0 "10 g 10 RSun = 7.0 "10 cm 3 #Sun =1.4 g/cm log g = GM /R2 = 4.44 [cgs]

! image credit: SOHO (ESA + NASA)

Feb 18, 2009 PHY 688, Lecture 11 15 Given Masses and Radii, Estimate Densities, Surface Gravities

• (M2 I)

M "10MSun

R "1000RSun $8 # "10 #Sun "1.4 %10$8 g/cm3 log g " $0.6

Feb 18, 2009 PHY 688, Lecture 11 16 ! Given Masses and Radii, Estimate Densities, Surface Gravities

• B ()

M " 0.6MSun

R " 0.01RSun 5 # " 6 $10 #Sun " 8 $105 g/cm3 log g " 8 B

credit: Hubble Space Telescope (NASA)

Feb 18, 2009 PHY 688, Lecture 11 17 ! Given Masses and Radii, Estimate Densities, Surface Gravities

• Gl 229B (T6.5)

M " 0.03MSun

R " 0.1RSun

# " 30#Sun " 40 g/cm3 log g " 5

Feb 18, 2009 PHY 688, Lecture 11 18 ! Given Masses and Radii, Estimate Densities, Surface Gravities • 2MASS 0535–0546B – secondary of first eclipsing substellar binary

M = 0.034MSun

R = 0.51RSun

" = 0.26"Sun = 0.36 g/cm3 log g = 3.6

Feb 18, 2009 PHY 688, Lecture 11 19 ! Given Masses and Radii, Estimate Densities, Surface Gravities •

#3 M = 0.95 "10 MSun

R = 0.10RSun

$ = 0.88$Sun =1.25 g/cm3 log g = 3.4

! Feb 18, 2009 PHY 688, Lecture 11 20 2M 0535–05A At Constant Mass Younger Brown (0.054 M ) Sun Dwarfs Have Lower Gravities

2MASS 0535–0546B (0.034 MSun) stars brown dwarfs “planets”

Gl 229B

(~0.03 MSun)

Feb 18, 2009 PHY 688, Lecture 11 (Burrows et al. 2001) 21 At Constant Teff Younger Brown Dwarfs Are Less Massive, Have Lower Gravities

stars brown dwarfs “planets” 2MASS 0535–0546 A/B M

13 M J 10 up M J up

5 M J stars up Gl 229B brown dwarfs “planets” 1 M Jup Jupiter

Feb 18, 2009 (Burrows et al. 2001) PHY 688, Lecture 11 22 At Constant Teff, Younger Brown Dwarfs

Have LGl o229Bwer Gravities

2MASS 0535–0546 A/B

Jupiter

log g vs. Teff for brown dwarfs and planets

Feb 18, 2009 PHY 688, Lecture 11 (Burrows et al. 1997) 23 Luminosity (i.e., Surface Gravity) Effects at A0

(figure: D. Gray) Feb 18, 2009 PHY 688, Lecture 11 24 From Lecture 5: Line Profiles # /2$ • Natural line width (Lorentzian [a.k.a., Cauchy] profile) I I " = 0 2 2 – Heisenberg uncertainty principle: ∆ν =∆E/h (" %" 0 ) + # /4 • Collisional broadening (Lorentzian profile) # & Lorentzian FWHM – collisions interrupt photon emission process #E i + #E f 1 1 –9 – ∆t < ∆t ~ 10 s " natural = = + coll emission h /2$ #t #t – dependent on T, ρ i f • Pressure broadening (~ Lorentzian profile) ! " collisional = 2 #tcoll – ∆t > ∆t &n interaction emission " pressure % r ; n = 2,3,4,6 – nearby particles shift energy levels of emitting particle • Stark effect (n = 2, 4) 2 (" %" 0 ) • van der Waals force (n = 6) cool stars % 1 2$ 2 • dipole coupling between pairs of same species (n = 3) I = e ! " 2#$ – dependent mostly on ρ, less on T • Thermal Doppler broadening (Gaussian profile) $ & Gaussian FWHM – emitting particles have a Maxwellian distribution of velocities kT "thermal = # 0 • Rotational Doppler broadening (Gaussian profile) mc 2 – radiation emitted from a spatially unresolved rotating! body "rotational = 2# 0u/c •Feb C18o, m200p9osite line profile: LorentziaPnH Y+ 6 8G8,a Luescstuirae n1 1= Voigt profile 25

! Feb 18, 2009 PHY 688, Lecture 11 (Kleinmann & Hall 1986) 26 Gravity-Sensitive Features in UCDs

Feb 18, 2009 PHY 688, Lecture 11 (McGovern et al. 2004) 27 Gravity in UCDs Key species: • neutral alkali elements (Na, K) – weaker at low g • hydrides – CaH weaker at low g – FeH unchanged • oxides – VO, CO, TiO stronger at low g

– H2O ~ unchanged log g and Teff are measurable properties Wavelength (µm) Feb 18, 2009 (Kirkpatrick et al. 2006) PHY 688, Lecture 11 28 Example: HR8799bcd – Do the “Planets” Have Planetary Masses?

Keck AO image of the HR 8799bcd planetary system (Marois et al. 2008, Science)

Feb 18, 2009 PHY 688, Lecture 11 29 Masses of HR8799bcd Gl 229B

2MASS 0535–0546 A/B

Jupiter

Can use log g and Teff to infer substellar mass

Feb 18, 2009 PHY 688, Lecture 11 (Burrows et al. 1997) 30