1Tsevi Mazeh: Leuven-Binaries 2 3 Double stars Rev. John Mitchell - 1767 it is highly probable in...
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Transcript of 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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Tsevi Mazeh: Leuven-Binaries 2
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Tsevi Mazeh: Leuven-Binaries 3
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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Tsevi Mazeh: Leuven-Binaries 4
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
![Page 5: 1Tsevi Mazeh: Leuven-Binaries 2 3 Double stars Rev. John Mitchell - 1767 it is highly probable in particular, and next to a certainty in general, that.](https://reader037.fdocuments.net/reader037/viewer/2022102814/551940465503468d738b4584/html5/thumbnails/5.jpg)
Tsevi Mazeh: Leuven-Binaries 5
Example of Visual Binaries
Krueger 60 : d = 4 pcM3.5V + M 4V, Period = 44.5 years
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Tsevi Mazeh: Leuven-Binaries 6
Example of Visual Binaries
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Tsevi Mazeh: Leuven-Binaries 7
a
d
( )a
radd
d
a
265,206
''
265,206)(
)(
265,206
''
pcd
a AU)(
)(''
pcd
a AU
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Tsevi Mazeh: Leuven-Binaries 8
23
GM
a
Sun
AU
YR
MMM
aP
21
3
21
1
Kepler’s 3rd law:
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Tsevi Mazeh: Leuven-Binaries 9
Ursa Major, The Big Bear (Big Dipper)
Mizar was the first known binary, noticed in 1650 by Riccioli.
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Tsevi Mazeh: Leuven-Binaries 10
Mizar: A binary within a binary
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Tsevi Mazeh: Leuven-Binaries 11
Resolution of a telescope
D
sec
1
5.01.0
arc
mD
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Tsevi Mazeh: Leuven-Binaries 12
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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Tsevi Mazeh: Leuven-Binaries 13
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Tsevi Mazeh: Leuven-Binaries 14
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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Tsevi Mazeh: Leuven-Binaries 15
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Tsevi Mazeh: Leuven-Binaries 16
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Tsevi Mazeh: Leuven-Binaries 17
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Tsevi Mazeh: Leuven-Binaries 18
Keck Interferometer (2x10m) Mauna Kea, Hawaii
VLT Interferometer (4x8m)
Chile (ESA)
Examples of Optical Interferometers
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Tsevi Mazeh: Leuven-Binaries 19
a1 a2
M1
M2
CM
2211 aMaM
The binary motion
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Tsevi Mazeh: Leuven-Binaries 20
21 MM
2M 1M
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Tsevi Mazeh: Leuven-Binaries 21
12 5.0 MM
2M1M
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Tsevi Mazeh: Leuven-Binaries 2212 1.0 MM
2M 1M
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Tsevi Mazeh: Leuven-Binaries 231001.0 MM Planet
1MPlanet
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Tsevi Mazeh: Leuven-Binaries 24
Kepler first law:
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Tsevi Mazeh: Leuven-Binaries 25
Kepler second law:
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Tsevi Mazeh: Leuven-Binaries 26
Origin of orbits of both stars
Periastron point
Empty
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Tsevi Mazeh: Leuven-Binaries 27
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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Tsevi Mazeh: Leuven-Binaries 28
Wobble of Sirius
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Tsevi Mazeh: Leuven-Binaries 29
Sirius AB Binary System
HST image
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Tsevi Mazeh: Leuven-Binaries 30
Orbits of Sirius A and B
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Tsevi Mazeh: Leuven-Binaries 31
Sirius AB Binary System
24.7 Vm
0013.01010 9.25.2/24.7
,
,
VA
VB
L
L
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Tsevi Mazeh: Leuven-Binaries 32
• 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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Tsevi Mazeh: Leuven-Binaries 33
• 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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Tsevi Mazeh: Leuven-Binaries 34
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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Tsevi Mazeh: Leuven-Binaries 35
The H-R Diagram
L = 4 R2 T4
425 ///107.5 Kscmerg
%)3(0084.0 SunB RR
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Tsevi Mazeh: Leuven-Binaries 36
The Sizes of Stars
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Tsevi Mazeh: Leuven-Binaries 37
Gliese 229B8’’ separation
10 mag difference in J,H,K
(Nakajima 1995)
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Tsevi Mazeh: Leuven-Binaries 38
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
![Page 39: 1Tsevi Mazeh: Leuven-Binaries 2 3 Double stars Rev. John Mitchell - 1767 it is highly probable in particular, and next to a certainty in general, that.](https://reader037.fdocuments.net/reader037/viewer/2022102814/551940465503468d738b4584/html5/thumbnails/39.jpg)
39Tsevi Mazeh: Leuven-Binaries
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40
One star with a spectrum composed of two spectra
Tsevi Mazeh: Leuven-Binaries
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41
The Doppler Effect
Spectrum of Hydrogen in Lab
Spectrum of a
Star
radv
c
Tsevi Mazeh: Leuven-Binaries
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42
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
Tsevi Mazeh: Leuven-Binaries
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21 MM
2M 1M
To earthTsevi Mazeh: Leuven-Binaries
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44
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.
Tsevi Mazeh: Leuven-Binaries
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Spectroscopic Binaries
Double-lined spectroscopic binary.
Tsevi Mazeh: Leuven-Binaries
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46
Spectroscopic Binaries
Tsevi Mazeh: Leuven-Binaries
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Tsevi Mazeh: Leuven-Binaries 47
Single-lined spectroscopic binary (SB1)
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Tsevi Mazeh: Leuven-Binaries 48
Single-lined spectroscopic binary (SB1)
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49Tsevi Mazeh: Leuven-Binaries
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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
Tsevi Mazeh: Leuven-Binaries
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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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53
)()( 1421 TTP
aRR
)()( 2321 TTP
aRR
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54
The geometry of the eclipse
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Tsevi Mazeh: Leuven-Binaries 55
Relative dimension: )()( 2321 TTP
aRR
Relative surface flux
Inclination
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56
CoRoT-Exo-2
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57Tsevi Mazeh: Leuven-Binaries
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Absolute Properties of the Main-Sequence Eclipsing Binary Star BP Vulpeculae
Tsevi Mazeh: Leuven-Binaries
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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