Binary Stars and
Fundamental Stellar Parameters
PHY 521, Lecture 26
Mass
• most fundamental
of stellar parameters
– L ∝ M3.8
– τMS ≈
1010 yr (M/MSun)–2.8
• impossible to
measure for isolated
stars
Dec 6, 2011
PHY 521, Lecture 26
2
Dynamical Masses:
Binary Stars to the Rescue
• ~ 1/3 of stars are binaries
• ~ 50% of Sun-like (~ 1 MSun) stars are binaries
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PHY 521, Lecture 26
3
Dynamical Masses:
Binary Stars to the Rescue
• Resolved visual binaries: see stars separately, measure
orbital axes and speeds directly.
• Astrometric binaries: only brighter member seen, with
periodic wobble in the track of its proper motion.
• Spectroscopic binaries: unresolved (relatively close)
binaries told apart by periodically oscillating Doppler
shifts in spectral lines. Periods = days to years.
– Eclipsing binaries: orbits seen nearly edge on, so that the stars
actually eclipse one another. (Most useful.)
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PHY 521, Lecture 26
4
Visual
Binary
• GJ 569Bab
binary
brown dwarf
• a > 5–10AU
(Lane et al. 2001)
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PHY 521, Lecture 26
5
First Dynamical Mass of T Dwarf
(Visual) Binary: 2MASS J1534–2952AB
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PHY 521, Lecture 26
(Liu et al., 2008)
6
Astrometric Binary
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7
Astrometric Binary: Sirius AB
• Sirius A:
– nearby luminous B star
– brightest star in the sky
• ~1 MSun white dwarf
companion first
inferred from its large
astrometric effect on
primary
• now also a visual
binary
Dec 6, 2011
B
Hubble Space Telescope image
PHY 521, Lecture 26
8
Astrometric Binary: GJ 802AB
• unseen
brown dwarf
companion
• a > 0.5–2AU
(Pravdo et al. 2005)
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PHY 521, Lecture 26
9
Spectroscopic
Binary
(a)
• double-lined (SB2)
– spectra of both stars visible
(d)
(a)
(b)
(b)
(c)
(c)
(d)
(d)
• single-lined (SB1)
– only spectrum of brighter star visible
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PHY 521, Lecture 26
10
Radial Velocity vs. Time for Doublelined SB in a Circular Orbit
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11
Radial Velocity vs. Time for Doublelined SB in Elliptical Orbit (e = 0.4)
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12
Spectroscopic Binary: 51 Peg Ab
(SB1)
• first planet detected
around a mainsequence star
– primary SpT: G2 V
• Mp sin i = 0.47 MJup
(Mayor & Queloz 1995)
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PHY 521, Lecture 26
13
Visual + Spectroscopic
Binary Brown Dwarf: Gl 569Bab
•
•
Dec 6, 2011
first BD dynamical mass
Mtot = 0.l25 ± 0.007 MSun
PHY 521, Lecture 26 (Lane et al. 2001; Simon et al. 2006) 14
Totally Eclipsing Binaries
Dec 6, 2011
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15
Totally Eclipsing Binaries
ta – start of secondary ingress
tb – end of secondary ingress
tc – start of secondary egress
td – end of secondary egress
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PHY 521, Lecture 26
16
Dynamical Mass Determination
– If orbital major axes (relative to center of mass) or radial
velocity amplitudes are known, so is the ratio of masses:
m1 a2 v2 r
=
=
m2 a1 v1r
– If the period, P, and the sum of semi-major axis lengths,
a = a1 + a2 , are known, Kepler’s third law can give
masses separately:
12
2
#
&
4"
P =%
a3 (
$ G(m1 + m2 ) '
Dec 6, 2011
PHY 521, Lecture 26
17
Dynamical Mass Determination
– If only the two radial velocities are known (SB2), the
sum of masses (from Kepler’s third law) is:
3
P ! v1r + v2 r $
m1 + m2 =
#
&
2'G " sin i %
– If only one radial velocity is known (SB1), a useful
quantity is the mass function:
3
3
v1 P ( m2 sin i)
f (m1,m2 ) =
=
2"G ( m1 + m2 ) 2
– If orientation angle of orbit, i, is known, this allows
determination of m2/m1
!
Dec 6, 2011
PHY 521, Lecture 26
18
Other Uses for Totally Eclipsing
Binary Systems: Radii and Teff’s
• Duration of eclipses and shape of light curve can be used to
determine radii of stars:
v1 + v2
=
(t2 ! t1 )
2
v1 + v2
Rl =
(t3 ! t1 )
2
(radius of R
s
secondary)
(radius of
primary)
t1 – start of secondary ingress
t2 – end of secondary ingress
t3 – start of secondary egress
Relative depth of primary (deepest) and secondary brightness
minima of eclipses can be used to determine the ratio of effective
temperatures of the stars:
F0 ! Fprimary
F0 ! Fsecondary
Dec 6, 2011
" Te ,s
=$
$ Te ,l
&
PHY 521, Lecture 26
#
%%
'
4
.
19
First Determination of
Substellar Radii
Dec 6, 2011
PHY 521, Lecture 26
(Stassun et al., 2005)
20
First Determination of
Substellar Radii
M2/M1 = 0.63 ± 0.09
T2/T1 = 1.054 ± 0.006 (!)
Dec 6, 2011
PHY 521, Lecture 26
(Stassun et al., 2005)
21
Luminosity-Mass Relation for Stars
with Well-determined Orbits
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PHY 521, Lecture 26
(Popper 1980)
22
Radius–Mass Relation for Eclipsing
Binaries with Well-Determined Orbits
100
Radius (R e )
10
1
Detached binaries
Semidetached/contact binaries
0.1
0.1
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1
10
Mass ( M e )
PHY 521, Lecture 26
100
(Malkov 1993)
23
Teff–Mass Relation for Eclipsing
Binaries with Well-determined Orbits
50000
Detached binaries
Temperature (K)
40000
Semidetached/contact binaries
30000
20000
10000
0
0.1
1
10
Mass ( M e )
Dec 6, 2011
PHY 521, Lecture 26
100
(Malkov 1993)
24
G Dwarf Binary Period Distribution
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Binary Separations
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PHY 521, Lecture 26
(Reid & Metchev 2007)
26
Binary Mass Ratio Distribution
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(Reid & Metchev 2007)
27
Roche Potential
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Roche Potential
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29