Fundamental (Sub)stellar Parameters: Surface Gravity PHY 688, Lecture 11
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 2
Previously in PHY 688 Feb 18, 2009 PHY 688, Lecture 11 3
Mass most fundamental of stellar parameters L M 3.8 τ MS 10 10 yr (M/M Sun ) 2.8 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: orbits 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 (+ a 1, a 2 if independent astrometric reference exists) determine: M tot (+ M 1, M 2 ) (Lane et al. 2001) a > 5 10AU Feb 18, 2009 PHY 688, Lecture 11 6
Astrometric Binary: GJ 802AB unseen brown dwarf com-panion; first and only to be discovered astrometrically measure: P, a 1, i (using independent astrometric reference) (Pravdo et al. 2005) determine: M 1 (a 2, M 2 can be constrained from resolved imaging) a > 0.5 2AU Feb 18, 2009 PHY 688, Lecture 11 7
Spectroscopic Binary double-lined (SB2) spectra of both stars visible (a) (b) (d) (a) (b) (c) (c) (d) single-lined (SB1) only spectrum of brighter star visible Feb 18, 2009 PHY 688, Lecture 11 8 (d)
Radial Velocity vs. Time for an SB2 in a Circular Orbit measure: P, v 1, v 2 determine: a 1 sin i, a 2 sin i, M 1 sin i, M 2 sin i Feb 18, 2009 PHY 688, Lecture 11 9
SB1 Spectroscopic Binary: 51 Peg Ab first planet detected around a mainsequence star primary SpT: G2 V M p sin i = 0.47 M Jup 0 AU < a < 10 AU measure: P, v (Mayor & Queloz 1995) 1 determine: a sin i, M 2 sin i (if M 1 approximately known) Feb 18, 2009 PHY 688, Lecture 11 10
Totally Eclipsing Binaries (Are Also SB1 s or SB2 s) t a start of secondary ingress t b end of secondary ingress t c start of secondary egress t d end of secondary egress measure: P, v 1, i, F 1, F 2 (+ v 2 if SB2) determine: a, M 1, M 2, R 1, R 2, ratio T eff,1 /T eff,2 M 1, M 2 determined exactly if SB2; otherwise, only ratio is known Feb 18, 2009 PHY 688, Lecture 11 11
First Determination of Substellar Radii: 2MASS 0535 0546 A/B (Stassun et al., 2005) Feb 18, 2009 PHY 688, Lecture 11 12
Luminosity-Mass Relation for Stars with Well-determined Orbits similar relations for radius and T eff 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 Densities, Surface Gravities Sun M Sun = 2.0 "10 33 g R Sun = 7.0 "10 10 cm # Sun =1.4 g/cm 3 log g = GM /R 2 = 4.44 [cgs] image credit: SOHO (ESA + NASA) Feb 18, 2009 PHY 688, Lecture 11 15
Given Masses and Radii, Estimate Densities, Surface Gravities Betelgeuse (M2 I) M " 10MSun R " 1000RSun # " 10$8 #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 Sirius B (white dwarf) M " 0.6M Sun R " 0.01R Sun # " 6 $10 5 # Sun " 8 $10 5 g/cm 3 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 " 0.03M Sun R " 0.1R Sun # " 30# Sun " 40 g/cm 3 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 = 0.034M Sun R = 0.51R Sun " = 0.26" Sun = 0.36 g/cm 3 log g = 3.6 Feb 18, 2009 PHY 688, Lecture 11 19
Given Masses and Radii, Estimate Jupiter Densities, Surface Gravities M = 0.95 "10 #3 M Sun R = 0.10R Sun $ = 0.88$ Sun =1.25 g/cm 3 log g = 3.4 Feb 18, 2009 PHY 688, Lecture 11 20
2M 0535 05A (0.054 M Sun ) At Constant Mass Younger Brown Dwarfs Have Lower Gravities 2MASS 0535 0546B (0.034 M Sun ) stars brown dwarfs planets Gl 229B (~0.03 M Sun ) (Burrows et al. 2001) Feb 18, 2009 PHY 688, Lecture 11 21
At Constant T eff Younger Brown Dwarfs Are Less Massive, Have Lower Gravities 2MASS 0535 0546 A/B M stars brown dwarfs planets 13 M Jup 10 M Jup 5 M Jup stars brown dwarfs planets Gl 229B 1 M Jup Jupiter Feb 18, 2009 PHY 688, Lecture 11 22 (Burrows et al. 2001)
At Constant T eff, Younger Brown Dwarfs Have Lower Gravities Gl 229B 2MASS 0535 0546 A/B Jupiter log g vs. T eff for brown dwarfs and planets Feb 18, 2009 PHY 688, Lecture 11 23 (Burrows et al. 1997)
Luminosity (i.e., Surface Gravity) Effects at A0 (figure: D. Gray) Feb 18, 2009 PHY 688, Lecture 11 24
From Lecture 5: Line Profiles Natural line width (Lorentzian [a.k.a., Cauchy] profile) Heisenberg uncertainty principle: ν = E/h Collisional broadening (Lorentzian profile) collisions interrupt photon emission process t coll < t emission ~ 10 9 s dependent on T, ρ Pressure broadening (~ Lorentzian profile) t interaction > t emission nearby particles shift energy levels of emitting particle Stark effect (n = 2, 4) van der Waals force (n = 6) cool stars dipole coupling between pairs of same species (n = 3) I " = dependent mostly on ρ, less on T Thermal Doppler broadening (Gaussian profile) emitting particles have a Maxwellian distribution of velocities Rotational Doppler broadening (Gaussian profile) radiation emitted from a spatially unresolved rotating body Composite line profile: Lorentzian + Gaussian = Voigt profile # /2$ I " = I 0 (" %" 0 ) 2 + # 2 /4 # & Lorentzian FWHM " natural = #E i + #E f h /2$ " collisional = 2 #t coll = 1 #t i + 1 #t f " pressure % r &n ; n = 2,3,4,6 (" %" 0 ) 2 2$ 2 1 2#$ e% $ & Gaussian FWHM " thermal = # 0 kt mc 2 " rotational = 2# 0 u /c Feb 18, 2009 PHY 688, Lecture 11 25
Feb 18, 2009 PHY 688, Lecture 11 26 (Kleinmann & Hall 1986)
Gravity-Sensitive Features in UCDs Feb 18, 2009 PHY 688, Lecture 11 27 (McGovern et al. 2004)
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 H 2 O ~ unchanged log g and T eff are measurable properties (Kirkpatrick et al. 2006) Wavelength (µm) Feb 18, 2009 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 T eff to infer substellar mass Feb 18, 2009 PHY 688, Lecture 11 30 (Burrows et al. 1997)