Binary Stars and Fundamental Stellar Parameters · Binary Systems: Radii and T eff ’s •Duration...

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Binary Stars and Fundamental Stellar Parameters PHY 521, Lecture 26

Transcript of Binary Stars and Fundamental Stellar Parameters · Binary Systems: Radii and T eff ’s •Duration...

Page 1: Binary Stars and Fundamental Stellar Parameters · Binary Systems: Radii and T eff ’s •Duration of eclipses and shape of light curve can be used to determine radii of stars: Relative

Binary Stars andFundamental Stellar Parameters

PHY 521, Lecture 26

Page 2: Binary Stars and Fundamental Stellar Parameters · Binary Systems: Radii and T eff ’s •Duration of eclipses and shape of light curve can be used to determine radii of stars: Relative

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

Page 3: Binary Stars and Fundamental Stellar Parameters · Binary Systems: Radii and T eff ’s •Duration of eclipses and shape of light curve can be used to determine radii of stars: Relative

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

Page 4: Binary Stars and Fundamental Stellar Parameters · Binary Systems: Radii and T eff ’s •Duration of eclipses and shape of light curve can be used to determine radii of stars: Relative

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.)

Page 5: Binary Stars and Fundamental Stellar Parameters · Binary Systems: Radii and T eff ’s •Duration of eclipses and shape of light curve can be used to determine radii of stars: Relative

Dec 6, 2011 PHY 521, Lecture 26 5

• GJ 569Babbinarybrown dwarf

• a > 5–10AU

VisualBinary

(Lane et al. 2001)

Page 6: Binary Stars and Fundamental Stellar Parameters · Binary Systems: Radii and T eff ’s •Duration of eclipses and shape of light curve can be used to determine radii of stars: Relative

Dec 6, 2011 PHY 521, Lecture 26 6

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

(Liu et al., 2008)

Page 7: Binary Stars and Fundamental Stellar Parameters · Binary Systems: Radii and T eff ’s •Duration of eclipses and shape of light curve can be used to determine radii of stars: Relative

Dec 6, 2011 PHY 521, Lecture 26 7

Astrometric Binary

Page 8: Binary Stars and Fundamental Stellar Parameters · Binary Systems: Radii and T eff ’s •Duration of eclipses and shape of light curve can be used to determine radii of stars: Relative

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

Page 9: Binary Stars and Fundamental Stellar Parameters · Binary Systems: Radii and T eff ’s •Duration of eclipses and shape of light curve can be used to determine radii of stars: Relative

Dec 6, 2011 PHY 521, Lecture 26 9

Astrometric Binary: GJ 802AB

• unseenbrown dwarfcompanion

• a > 0.5–2AU

(Pravdo et al. 2005)

Page 10: Binary Stars and Fundamental Stellar Parameters · Binary Systems: Radii and T eff ’s •Duration of eclipses and shape of light curve can be used to determine radii of stars: Relative

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)

Page 11: Binary Stars and Fundamental Stellar Parameters · Binary Systems: Radii and T eff ’s •Duration of eclipses and shape of light curve can be used to determine radii of stars: Relative

Dec 6, 2011 PHY 521, Lecture 26 11

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

Page 12: Binary Stars and Fundamental Stellar Parameters · Binary Systems: Radii and T eff ’s •Duration of eclipses and shape of light curve can be used to determine radii of stars: Relative

Dec 6, 2011 PHY 521, Lecture 26 12

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

Page 13: Binary Stars and Fundamental Stellar Parameters · Binary Systems: Radii and T eff ’s •Duration of eclipses and shape of light curve can be used to determine radii of stars: Relative

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)

Page 14: Binary Stars and Fundamental Stellar Parameters · Binary Systems: Radii and T eff ’s •Duration of eclipses and shape of light curve can be used to determine radii of stars: Relative

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)

Page 15: Binary Stars and Fundamental Stellar Parameters · Binary Systems: Radii and T eff ’s •Duration of eclipses and shape of light curve can be used to determine radii of stars: Relative

Dec 6, 2011 PHY 521, Lecture 26 15

Totally Eclipsing Binaries

Page 16: Binary Stars and Fundamental Stellar Parameters · Binary Systems: Radii and T eff ’s •Duration of eclipses and shape of light curve can be used to determine radii of stars: Relative

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

Page 17: Binary Stars and Fundamental Stellar Parameters · Binary Systems: Radii and T eff ’s •Duration of eclipses and shape of light curve can be used to determine radii of stars: Relative

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= +

Page 18: Binary Stars and Fundamental Stellar Parameters · Binary Systems: Radii and T eff ’s •Duration of eclipses and shape of light curve can be used to determine radii of stars: Relative

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

Page 19: Binary Stars and Fundamental Stellar Parameters · Binary Systems: Radii and T eff ’s •Duration of eclipses and shape of light curve can be used to determine radii of stars: Relative

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)

Page 20: Binary Stars and Fundamental Stellar Parameters · Binary Systems: Radii and T eff ’s •Duration of eclipses and shape of light curve can be used to determine radii of stars: Relative

Dec 6, 2011 PHY 521, Lecture 26 20

First Determination ofSubstellar Radii

(Stassun et al., 2005)

Page 21: Binary Stars and Fundamental Stellar Parameters · Binary Systems: Radii and T eff ’s •Duration of eclipses and shape of light curve can be used to determine radii of stars: Relative

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 (!)

Page 22: Binary Stars and Fundamental Stellar Parameters · Binary Systems: Radii and T eff ’s •Duration of eclipses and shape of light curve can be used to determine radii of stars: Relative

Dec 6, 2011 PHY 521, Lecture 26 22

Luminosity-Mass Relation for Starswith Well-determined Orbits

(Popper 1980)

Page 23: Binary Stars and Fundamental Stellar Parameters · Binary Systems: Radii and T eff ’s •Duration of eclipses and shape of light curve can be used to determine radii of stars: Relative

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)

Page 24: Binary Stars and Fundamental Stellar Parameters · Binary Systems: Radii and T eff ’s •Duration of eclipses and shape of light curve can be used to determine radii of stars: Relative

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)

Page 25: Binary Stars and Fundamental Stellar Parameters · Binary Systems: Radii and T eff ’s •Duration of eclipses and shape of light curve can be used to determine radii of stars: Relative

Dec 6, 2011 PHY 521, Lecture 26 25

G Dwarf Binary Period Distribution

Page 26: Binary Stars and Fundamental Stellar Parameters · Binary Systems: Radii and T eff ’s •Duration of eclipses and shape of light curve can be used to determine radii of stars: Relative

Dec 6, 2011 PHY 521, Lecture 26 26

Binary Separations

(Reid & Metchev 2007)

Page 27: Binary Stars and Fundamental Stellar Parameters · Binary Systems: Radii and T eff ’s •Duration of eclipses and shape of light curve can be used to determine radii of stars: Relative

Dec 6, 2011 PHY 521, Lecture 26 27

Binary Mass Ratio Distribution

(Reid & Metchev 2007)

Page 28: Binary Stars and Fundamental Stellar Parameters · Binary Systems: Radii and T eff ’s •Duration of eclipses and shape of light curve can be used to determine radii of stars: Relative

Dec 6, 2011 PHY 521, Lecture 26 28

Roche Potential

Page 29: Binary Stars and Fundamental Stellar Parameters · Binary Systems: Radii and T eff ’s •Duration of eclipses and shape of light curve can be used to determine radii of stars: Relative

Dec 6, 2011 PHY 521, Lecture 26 29

Roche Potential