Fundamental (Sub)stellar Parameters: Surface Gravity
Transcript of Fundamental (Sub)stellar Parameters: Surface Gravity
![Page 1: Fundamental (Sub)stellar Parameters: Surface Gravity](https://reader030.fdocuments.net/reader030/viewer/2022012519/61934028695881593c74c5ab/html5/thumbnails/1.jpg)
Fundamental (Sub)stellar Parameters:Surface Gravity
PHY 688, Lecture 11
![Page 2: Fundamental (Sub)stellar Parameters: Surface Gravity](https://reader030.fdocuments.net/reader030/viewer/2022012519/61934028695881593c74c5ab/html5/thumbnails/2.jpg)
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
![Page 3: Fundamental (Sub)stellar Parameters: Surface Gravity](https://reader030.fdocuments.net/reader030/viewer/2022012519/61934028695881593c74c5ab/html5/thumbnails/3.jpg)
Feb 18, 2009 PHY 688, Lecture 11 3
Previously in PHY 688…
![Page 4: Fundamental (Sub)stellar Parameters: Surface Gravity](https://reader030.fdocuments.net/reader030/viewer/2022012519/61934028695881593c74c5ab/html5/thumbnails/4.jpg)
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
![Page 5: Fundamental (Sub)stellar Parameters: Surface Gravity](https://reader030.fdocuments.net/reader030/viewer/2022012519/61934028695881593c74c5ab/html5/thumbnails/5.jpg)
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.)
![Page 6: Fundamental (Sub)stellar Parameters: Surface Gravity](https://reader030.fdocuments.net/reader030/viewer/2022012519/61934028695881593c74c5ab/html5/thumbnails/6.jpg)
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)
![Page 7: Fundamental (Sub)stellar Parameters: Surface Gravity](https://reader030.fdocuments.net/reader030/viewer/2022012519/61934028695881593c74c5ab/html5/thumbnails/7.jpg)
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)
![Page 8: Fundamental (Sub)stellar Parameters: Surface Gravity](https://reader030.fdocuments.net/reader030/viewer/2022012519/61934028695881593c74c5ab/html5/thumbnails/8.jpg)
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)
![Page 9: Fundamental (Sub)stellar Parameters: Surface Gravity](https://reader030.fdocuments.net/reader030/viewer/2022012519/61934028695881593c74c5ab/html5/thumbnails/9.jpg)
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
![Page 10: Fundamental (Sub)stellar Parameters: Surface Gravity](https://reader030.fdocuments.net/reader030/viewer/2022012519/61934028695881593c74c5ab/html5/thumbnails/10.jpg)
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)
![Page 11: Fundamental (Sub)stellar Parameters: Surface Gravity](https://reader030.fdocuments.net/reader030/viewer/2022012519/61934028695881593c74c5ab/html5/thumbnails/11.jpg)
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
![Page 12: Fundamental (Sub)stellar Parameters: Surface Gravity](https://reader030.fdocuments.net/reader030/viewer/2022012519/61934028695881593c74c5ab/html5/thumbnails/12.jpg)
Feb 18, 2009 PHY 688, Lecture 11 12
First Determination of SubstellarRadii: 2MASS 0535–0546 A/B
(Stassun et al., 2005)
![Page 13: Fundamental (Sub)stellar Parameters: Surface Gravity](https://reader030.fdocuments.net/reader030/viewer/2022012519/61934028695881593c74c5ab/html5/thumbnails/13.jpg)
Feb 18, 2009 PHY 688, Lecture 11 13
Luminosity-Mass Relation for Starswith Well-determined Orbits
(Popper 1980)
similar relationsfor radius andTeff dependenceon mass
![Page 14: Fundamental (Sub)stellar Parameters: Surface Gravity](https://reader030.fdocuments.net/reader030/viewer/2022012519/61934028695881593c74c5ab/html5/thumbnails/14.jpg)
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
![Page 15: Fundamental (Sub)stellar Parameters: Surface Gravity](https://reader030.fdocuments.net/reader030/viewer/2022012519/61934028695881593c74c5ab/html5/thumbnails/15.jpg)
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
![Page 16: Fundamental (Sub)stellar Parameters: Surface Gravity](https://reader030.fdocuments.net/reader030/viewer/2022012519/61934028695881593c74c5ab/html5/thumbnails/16.jpg)
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
![Page 17: Fundamental (Sub)stellar Parameters: Surface Gravity](https://reader030.fdocuments.net/reader030/viewer/2022012519/61934028695881593c74c5ab/html5/thumbnails/17.jpg)
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
![Page 18: Fundamental (Sub)stellar Parameters: Surface Gravity](https://reader030.fdocuments.net/reader030/viewer/2022012519/61934028695881593c74c5ab/html5/thumbnails/18.jpg)
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
![Page 19: Fundamental (Sub)stellar Parameters: Surface Gravity](https://reader030.fdocuments.net/reader030/viewer/2022012519/61934028695881593c74c5ab/html5/thumbnails/19.jpg)
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
![Page 20: Fundamental (Sub)stellar Parameters: Surface Gravity](https://reader030.fdocuments.net/reader030/viewer/2022012519/61934028695881593c74c5ab/html5/thumbnails/20.jpg)
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
![Page 21: Fundamental (Sub)stellar Parameters: Surface Gravity](https://reader030.fdocuments.net/reader030/viewer/2022012519/61934028695881593c74c5ab/html5/thumbnails/21.jpg)
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)
![Page 22: Fundamental (Sub)stellar Parameters: Surface Gravity](https://reader030.fdocuments.net/reader030/viewer/2022012519/61934028695881593c74c5ab/html5/thumbnails/22.jpg)
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
![Page 23: Fundamental (Sub)stellar Parameters: Surface Gravity](https://reader030.fdocuments.net/reader030/viewer/2022012519/61934028695881593c74c5ab/html5/thumbnails/23.jpg)
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
![Page 24: Fundamental (Sub)stellar Parameters: Surface Gravity](https://reader030.fdocuments.net/reader030/viewer/2022012519/61934028695881593c74c5ab/html5/thumbnails/24.jpg)
Feb 18, 2009 PHY 688, Lecture 11 24
Luminosity (i.e., Surface Gravity)Effects at A0
(figure: D. Gray)
![Page 25: Fundamental (Sub)stellar Parameters: Surface Gravity](https://reader030.fdocuments.net/reader030/viewer/2022012519/61934028695881593c74c5ab/html5/thumbnails/25.jpg)
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
![Page 26: Fundamental (Sub)stellar Parameters: Surface Gravity](https://reader030.fdocuments.net/reader030/viewer/2022012519/61934028695881593c74c5ab/html5/thumbnails/26.jpg)
Feb 18, 2009 PHY 688, Lecture 11 26(Kleinmann & Hall 1986)
![Page 27: Fundamental (Sub)stellar Parameters: Surface Gravity](https://reader030.fdocuments.net/reader030/viewer/2022012519/61934028695881593c74c5ab/html5/thumbnails/27.jpg)
Feb 18, 2009 PHY 688, Lecture 11 27
Gravity-Sensitive Features in UCDs
(McGovern et al. 2004)
![Page 28: Fundamental (Sub)stellar Parameters: Surface Gravity](https://reader030.fdocuments.net/reader030/viewer/2022012519/61934028695881593c74c5ab/html5/thumbnails/28.jpg)
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
![Page 29: Fundamental (Sub)stellar Parameters: Surface Gravity](https://reader030.fdocuments.net/reader030/viewer/2022012519/61934028695881593c74c5ab/html5/thumbnails/29.jpg)
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)
![Page 30: Fundamental (Sub)stellar Parameters: Surface Gravity](https://reader030.fdocuments.net/reader030/viewer/2022012519/61934028695881593c74c5ab/html5/thumbnails/30.jpg)
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