Fundamental (Sub)stellar Parameters:Surface Gravity
PHY 688, Lecture 11
Feb 18, 2009 PHY 688, Lecture 11 2
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 3
Previously in PHY 688…
Feb 18, 2009 PHY 688, Lecture 11 4
Mass
• most fundamentalof stellar parameters– L ∝ M3.8
– τMS ≈1010 yr (M/MSun)–2.8
• impossible tomeasure for isolatedstars
Feb 18, 2009 PHY 688, Lecture 11 5
Dynamical Masses:Binary Stars to the Rescue
• Resolved visual binaries: see stars separately, measureorbital axes and speeds directly.
• Astrometric binaries: only brighter member seen, withperiodic wobble in the track of its proper motion.
• Spectroscopic binaries: unresolved (relatively close)binaries told apart by periodically oscillating Dopplershifts 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 6
• first with a dynamicalmass
• measure: P, a, i(+ a1, a2 ifindependentastrometric referenceexists)
• determine: Mtot
(+ M1, M2)
• a > 5–10AU
Visual Binary: GJ 569Bab
(Lane et al. 2001)
Feb 18, 2009 PHY 688, Lecture 11 7
Astrometric Binary: GJ 802AB• unseen brown
dwarf com-panion;first and only to bediscoveredastrometrically
• measure: P, a1, i(using independentastrometricreference)
• determine: M1(a2, M2 can beconstrained fromresolved imaging)
• a > 0.5–2AU(Pravdo et al. 2005)
Feb 18, 2009 PHY 688, Lecture 11 8
SpectroscopicBinary
• double-lined (SB2)– spectra of both stars visible
• single-lined (SB1)– only spectrum of brighter star visible
(a)
(b)
(c)
(d)
(a)(d) (b)
(c)
(d)
Feb 18, 2009 PHY 688, Lecture 11 9
Radial Velocity vs. Time for an SB2in a Circular Orbit
• measure: P, v1, v2• determine: a1 sin i, a2 sin i, M1 sin i, M2 sin i
Feb 18, 2009 PHY 688, Lecture 11 10
SB1 Spectroscopic Binary: 51 Peg Ab
• first planet detectedaround a main-sequence star– primary SpT: G2 V
• Mp sin i = 0.47 MJup
• 0 AU < a < 10 AU
• measure: P, v1• determine: a sin i, M2 sin i (if M1 approximately known)
(Mayor & Queloz 1995)
Feb 18, 2009 PHY 688, Lecture 11 11
Totally Eclipsing Binaries(Are Also SB1’s or SB2’s)
ta – start of secondary ingresstb – end of secondary ingresstc – start of secondary egresstd – end of secondary egress
• measure: P, v1, i, ∆F1, ∆F2 (+ v2 if SB2)• determine: a, M1, M2, R1, R2, ratio Teff,1/Teff,2
– M1, M2 determined exactly if SB2; otherwise, only ratio is known
Feb 18, 2009 PHY 688, Lecture 11 12
First Determination of SubstellarRadii: 2MASS 0535–0546 A/B
(Stassun et al., 2005)
Feb 18, 2009 PHY 688, Lecture 11 13
Luminosity-Mass Relation for Starswith Well-determined Orbits
(Popper 1980)
similar relationsfor radius andTeff dependenceon mass
Feb 18, 2009 PHY 688, Lecture 11 14
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 15
• Sun
!
MSun = 2.0 "1033 g
RSun = 7.0 "1010 cm
# Sun =1.4 g/cm3
log g =GM /R2= 4.44 [cgs]
image credit: SOHO (ESA + NASA)
Given Masses and Radii, EstimateDensities, Surface Gravities
Feb 18, 2009 PHY 688, Lecture 11 16
Given Masses and Radii, EstimateDensities, Surface Gravities
• Betelgeuse (M2 I)
!
M "10MSun
R "1000RSun
# "10$8# Sun
"1.4 %10$8g/cm3
log g " $0.6
Feb 18, 2009 PHY 688, Lecture 11 17
• Sirius B (white dwarf)
!
M " 0.6MSun
R " 0.01RSun
# " 6 $105# Sun
" 8 $105 g/cm3
log g " 8
credit: Hubble Space Telescope (NASA)
B
Given Masses and Radii, EstimateDensities, Surface Gravities
Feb 18, 2009 PHY 688, Lecture 11 18
• Gl 229B (T6.5)
!
M " 0.03MSun
R " 0.1RSun
# " 30# Sun
" 40 g/cm3
log g " 5
Given Masses and Radii, EstimateDensities, Surface Gravities
Feb 18, 2009 PHY 688, Lecture 11 19
• 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
Given Masses and Radii, EstimateDensities, Surface Gravities
Feb 18, 2009 PHY 688, Lecture 11 20
• Jupiter
!
M = 0.95 "10#3MSun
R = 0.10RSun
$ = 0.88$ Sun
=1.25 g/cm3
log g = 3.4
Given Masses and Radii, EstimateDensities, Surface Gravities
Feb 18, 2009 PHY 688, Lecture 11 21
At Constant Mass Younger BrownDwarfs Have Lower Gravities
starsbrown dwarfs“planets”
(Burrows et al. 2001)
Gl 229B(~0.03 MSun)
2MASS 0535–0546B (0.034 MSun)
2M 0535–05A
(0.054 MSun)
Feb 18, 2009 PHY 688, Lecture 11 22
At Constant Teff Younger Brown DwarfsAre Less Massive, Have Lower Gravities
starsbrown dwarfs“planets”
13 MJup10 M
Jup
5 MJup
1 MJup
starsbrown dwarfs“planets”
M
(Burrows et al. 2001)
Gl 229B
2MASS 0535–0546 A/B
Jupiter
Feb 18, 2009 PHY 688, Lecture 11 23
At Constant Teff, Younger Brown DwarfsHave Lower Gravities
(Burrows et al. 1997)
log g vs. Teff for brown dwarfs and planets
2MASS 0535–0546 A/B
Gl 229B
Jupiter
Feb 18, 2009 PHY 688, Lecture 11 24
Luminosity (i.e., Surface Gravity)Effects at A0
(figure: D. Gray)
Feb 18, 2009 PHY 688, Lecture 11 25
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– ∆tcoll < ∆temission ~ 10–9 s– dependent on T, ρ
• Pressure broadening (~ Lorentzian profile)– ∆tinteraction > ∆temission– nearby particles shift energy levels of emitting particle
• Stark effect (n = 2, 4)• van der Waals force (n = 6)• dipole coupling between pairs of same species (n = 3)
– 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
!
I" =1
2#$e
%" %"
0( )2
2$2
$ &Gaussian FWHM
!
"thermal
= #0
kT
mc2
"rotational
= 2#0u /c
!
" natural =#Ei + #E f
h /2$=1
#ti+1
#t f
" collisional = 2 #tcoll
" pressure % r&n; n = 2,3,4,6
!
I" = I0
# /2$
" %"0( )
2
+ # 2/4
# & Lorentzian FWHM
cool stars
Feb 18, 2009 PHY 688, Lecture 11 26(Kleinmann & Hall 1986)
Feb 18, 2009 PHY 688, Lecture 11 27
Gravity-Sensitive Features in UCDs
(McGovern et al. 2004)
Feb 18, 2009 PHY 688, Lecture 11 28
Gravity inUCDs
(Kirkpatrick et al. 2006)Wavelength (µm)
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
Feb 18, 2009 PHY 688, Lecture 11 29
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 30
Masses of HR8799bcd
(Burrows et al. 1997)
Can use log g and Teffto infer substellar mass
2MASS 0535–0546 A/B
Gl 229B
Jupiter