1tsevi mazeh: leuven-binaries 2 3 double stars rev. john mitchell - 1767 it is highly probable in...
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Tsevi Mazeh: Leuven-Binaries 1
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Double stars
Rev. John Mitchell - 1767
“it is highly probable in particular, and next to a certainty
in general, that such double stars as appear to consist
of two or more stars placed very near together, do really
consist of stars placed near together, and under the
influence of some general law.”
The definitive existence of binary stars was demonstrated by William Herschel in 1802.
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A multitude of types
Binary stars
astrometric eclipsing
spectroscopicVisual
Resolved bytelescope into
two starsOscillatorymotion on
the sky
Stars periodicallypass in front ofeach other in
our LOS
Unresolvedby telescope,but two setsof spectrallines seen
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Example of Visual Binaries
Krueger 60 : d = 4 pcM3.5V + M 4V, Period = 44.5 years
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Example of Visual Binaries
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a
d
( )a
radd
d
a
265,206
''
265,206)(
)(
265,206
''
pcd
a AU)(
)(''
pcd
a AU
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23
GM
a
Sun
AU
YR
MMM
aP
21
3
21
1
Kepler’s 3rd law:
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Ursa Major, The Big Bear (Big Dipper)
Mizar was the first known binary, noticed in 1650 by Riccioli.
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Mizar: A binary within a binary
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Resolution of a telescope
D
sec
1
5.01.0
arc
mD
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Binary system Mizar A Observed by NPOI
Navy Prototype Optical Interferometer (NPOI) Array south of Flagstaff AZ, The Mizar images were obtained with the inner three 0.5m telescopes. A total of 10 telescopes will be operational starting in 2003.
Mizar A binary (period 20 days).
0.01 arcsec
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Example:
Wavelength λ=500nm, baseline B=100m
Θ ~ 0.001“ = 1 mas
D
• CHARA – Center for High Angular Resolution Astronomy at Georgia State University
• SUSI – Sydney University Stellar Interferometer• NPOI - Navy Prototype Optical Interferometer • Mark III Interferometer• PTI - Palomar Testbed Interferometer
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Keck Interferometer (2x10m) Mauna Kea, Hawaii
VLT Interferometer (4x8m)
Chile (ESA)
Examples of Optical Interferometers
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a1 a2
M1
M2
CM
2211 aMaM
The binary motion
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21 MM
2M 1M
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12 5.0 MM
2M1M
Tsevi Mazeh: Leuven-Binaries 2212 1.0 MM
2M 1M
Tsevi Mazeh: Leuven-Binaries 231001.0 MM Planet
1MPlanet
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Kepler first law:
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Kepler second law:
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Origin of orbits of both stars
Periastron point
Empty
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The Masses of Sirius A & B
– 5th closest star to us: d = 2.63pc– Sirius A is the brightest star in the sky
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Wobble of Sirius
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Sirius AB Binary System
HST image
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Orbits of Sirius A and B
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Sirius AB Binary System
24.7 Vm
0013.01010 9.25.2/24.7
,
,
VA
VB
L
L
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• Ratio of motion:
3.23.2
1
1
1
2
2
1 a
a
a
a
M
M
Distance estimate:
a = 7.62” 20.04 AU at a distance of 2.63 pc
M1 + M2 = (20.04)3/(49.9)2 = 3.23
Kepler’s 3rd law:
Sirius AB Binary System
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• HenceM1 / M2 = 2.3 and M1 + M2 = 3.23
– so, unraveling the masses gives
M1 = mass of Sirius A = 2.25 M
M2 = mass of Sirius B = 0.98 M
Sirius AB Binary System
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1915-Adams obtained a spectrum of Sirius B T~25,000 K
1862- Clark resolved the two stars
Sirius AB Binary System
%)3(0084.0 SunB RR
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The H-R Diagram
L = 4 R2 T4
425 ///107.5 Kscmerg
%)3(0084.0 SunB RR
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The Sizes of Stars
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Gliese 229B8’’ separation
10 mag difference in J,H,K
(Nakajima 1995)
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A multitude of types
Binary stars
astrometric eclipsing
spectroscopicVisual
Resolved bytelescope into
two starsOscillatorymotion on
the sky
Stars periodicallypass in front ofeach other in
our LOS
Unresolvedby telescope,but two setsof spectrallines seen
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One star with a spectrum composed of two spectra
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The Doppler Effect
Spectrum of Hydrogen in Lab
Spectrum of a
Star
radv
c
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Spectroscopic binary
Spectrum of Hydrogen in Lab
Spectrum a Star…..Day 1
Spectrum a Star…..Day 2
Spectrum a Star…..Day 3
Spectrum a Star…..Day 4
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21 MM
2M 1M
To earthTsevi Mazeh: Leuven-Binaries
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Spectroscopic Binaries
If the Doppler shift of a star’s absorption lines changes with time (redshift, then blueshift, then redshift, etc.), it’s a spectroscopic binary.
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Spectroscopic Binaries
Double-lined spectroscopic binary.
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Spectroscopic Binaries
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Single-lined spectroscopic binary (SB1)
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Single-lined spectroscopic binary (SB1)
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Eclipsing Binaries
Animation Tsevi Mazeh: Leuven-Binaries
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• Time T1 = first contact
• Time T2 = beginning of total eclipse
• Time T3 = end of total eclipse phase
• Time T4 = last contact
Time
Bri
ghtn
ess
T1 T2 T3 T4
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Star ofradius R1
Star of radius R2
a
Orbit ofstar 2relativeto star 1
Eclipsezone
T1
T2 T3 T4
LOS
1 24 1 2
rel
R RT T
V
1 23 2 2
rel
R RT T
V
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)()( 1421 TTP
aRR
)()( 2321 TTP
aRR
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The geometry of the eclipse
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Relative dimension: )()( 2321 TTP
aRR
Relative surface flux
Inclination
56
CoRoT-Exo-2
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Absolute Properties of the Main-Sequence Eclipsing Binary Star BP Vulpeculae
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Lacy et al. 2003
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BP VULPECULAE
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BP VULPECULAE
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BP VULPECULAE
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BP VULPECULAE
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