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