Binary Stars andFundamental Stellar Parameters

PHY 521, Lecture 26

Dec 6, 2011 PHY 521, Lecture 26 2

Mass

• most fundamentalof stellar parameters– L ∝ M3.8

– τMS ≈1010 yr (M/MSun)–2.8

• impossible tomeasure for isolatedstars

Dec 6, 2011 PHY 521, Lecture 26 3

Dynamical Masses:Binary Stars to the Rescue

• ~ 1/3 of stars are binaries• ~ 50% of Sun-like (~ 1 MSun) stars are binaries

Dec 6, 2011 PHY 521, Lecture 26 4

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.)

Dec 6, 2011 PHY 521, Lecture 26 5

• GJ 569Babbinarybrown dwarf

• a > 5–10AU

VisualBinary

(Lane et al. 2001)

Dec 6, 2011 PHY 521, Lecture 26 6

First Dynamical Mass of T Dwarf(Visual) Binary: 2MASS J1534–2952AB

(Liu et al., 2008)

Dec 6, 2011 PHY 521, Lecture 26 7

Astrometric Binary

Dec 6, 2011 PHY 521, Lecture 26 8

Astrometric Binary: Sirius AB

• Sirius A:– nearby luminous B star– brightest star in the sky

• ~1 MSun white dwarfcompanion firstinferred from its largeastrometric effect onprimary

• now also a visualbinary Hubble Space Telescope image

B

Dec 6, 2011 PHY 521, Lecture 26 9

Astrometric Binary: GJ 802AB

• unseenbrown dwarfcompanion

• a > 0.5–2AU

(Pravdo et al. 2005)

Dec 6, 2011 PHY 521, Lecture 26 10

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)

Dec 6, 2011 PHY 521, Lecture 26 11

Radial Velocity vs. Time for Double-lined SB in a Circular Orbit

Dec 6, 2011 PHY 521, Lecture 26 12

Radial Velocity vs. Time for Double-lined SB in Elliptical Orbit (e = 0.4)

Dec 6, 2011 PHY 521, Lecture 26 13

Spectroscopic Binary: 51 Peg Ab(SB1)

• first planet detectedaround a main-sequence star– primary SpT: G2 V

• Mp sin i = 0.47 MJup

(Mayor & Queloz 1995)

Dec 6, 2011 PHY 521, Lecture 26 14

Visual + SpectroscopicBinary Brown Dwarf: Gl 569Bab

• first BD dynamical mass• Mtot = 0.l25 ± 0.007 MSun

(Lane et al. 2001; Simon et al. 2006)

Dec 6, 2011 PHY 521, Lecture 26 15

Totally Eclipsing Binaries

Dec 6, 2011 PHY 521, Lecture 26 16

Totally Eclipsing Binaries

ta – start of secondary ingresstb – end of secondary ingresstc – start of secondary egresstd – end of secondary egress

Dec 6, 2011 PHY 521, Lecture 26 17

Dynamical Mass Determination

– If orbital major axes (relative to center of mass) or radialvelocity amplitudes are known, so is the ratio of masses:

– If the period, P, and the sum of semi-major axis lengths, are known, Kepler’s third law can givemasses separately:

m

m

a

a

v

v

r

r

1

2

2

1

2

1

= =

!

P =4" 2

G(m1

+ m2)a3

#

$ %

&

' (

1 2

1 2 ,a a a= +

Dec 6, 2011 PHY 521, Lecture 26 18

Dynamical Mass Determination– If only the two radial velocities are known (SB2), the

sum of masses (from Kepler’s third law) is:

– If only one radial velocity is known (SB1), a usefulquantity is the mass function:

– If orientation angle of orbit, i, is known, this allowsdetermination of m2/m1

m mP

G

v v

i

r r

1 2

1 2

3

2+ =

+!"#

$%&

' sin

!

f (m1,m2) =v1

3P

2"G=m2 sin i( )

3

m1 + m2( )2

Dec 6, 2011 PHY 521, Lecture 26 19

Other Uses for Totally EclipsingBinary Systems: Radii and Teff’s

• Duration of eclipses and shape of light curve can be used todetermine radii of stars:

Relative depth of primary (deepest) and secondary brightnessminima of eclipses can be used to determine the ratio of effectivetemperatures of the stars:

( )

( )

1 22 1

1 23 1

2

2

s

v vR t t

v vR t t

+= !

+= !l

40 primary ,

0 secondary ,

.e s

e

F F T

F F T

! " #= $ %$ %! & 'l

t1 – start of secondary ingresst2 – end of secondary ingresst3 – start of secondary egress

(radius of secondary)(radius of primary)

Dec 6, 2011 PHY 521, Lecture 26 20

First Determination ofSubstellar Radii

(Stassun et al., 2005)

Dec 6, 2011 PHY 521, Lecture 26 21

First Determination ofSubstellar Radii

(Stassun et al., 2005)

M2/M1 = 0.63 ± 0.09T2/T1 = 1.054 ± 0.006 (!)

Dec 6, 2011 PHY 521, Lecture 26 22

Luminosity-Mass Relation for Starswith Well-determined Orbits

(Popper 1980)

Dec 6, 2011 PHY 521, Lecture 26 23

Radius–Mass Relation for EclipsingBinaries with Well-Determined Orbits

0.1

1

10

100

0.1 1 10 100

Mass (M e )

Rad

ius

( Re

)

Detached binaries

Semidetached/contact binaries

(Malkov 1993)

Dec 6, 2011 PHY 521, Lecture 26 24

Teff–Mass Relation for EclipsingBinaries with Well-determined Orbits

0

10000

20000

30000

40000

50000

0.1 1 10 100

Mass (M e )

Tem

per

atu

re (

K)

Detached binaries

Semidetached/contact binaries

(Malkov 1993)

Dec 6, 2011 PHY 521, Lecture 26 25

G Dwarf Binary Period Distribution

Dec 6, 2011 PHY 521, Lecture 26 26

Binary Separations

(Reid & Metchev 2007)

Dec 6, 2011 PHY 521, Lecture 26 27

Binary Mass Ratio Distribution

(Reid & Metchev 2007)

Dec 6, 2011 PHY 521, Lecture 26 28

Roche Potential

Dec 6, 2011 PHY 521, Lecture 26 29

Roche Potential