1Tsevi Mazeh: Leuven-Binaries 2 3 Double stars Rev. John Mitchell - 1767 it is highly probable in...

Tsevi Mazeh: Leuven-Binaries 1


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.


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


Example of Visual Binaries

Krueger 60 : d = 4 pcM3.5V + M 4V, Period = 44.5 years


Example of Visual Binaries


a

d

( )a

radd

d

a

265,206

''

265,206)(

)(

265,206

''

pcd

a AU)(

)(''

pcd

a AU


23

GM

a

Sun

AU

YR

MMM

aP

21

3

21

1

Kepler’s 3rd law:


Ursa Major, The Big Bear (Big Dipper)

Mizar was the first known binary, noticed in 1650 by Riccioli.


Mizar: A binary within a binary


Resolution of a telescope

D

sec

1

5.01.0

arc

mD


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

http://antwrp.gsfc.nasa.gov/apod/image/9702/mizarA_npoi_big.gif


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


Keck Interferometer (2x10m) Mauna Kea, Hawaii

VLT Interferometer (4x8m)

Chile (ESA)

Examples of Optical Interferometers


a1 a2

M1

M2

CM

2211 aMaM

The binary motion


21 MM

2M 1M


12 5.0 MM

2M1M

Tsevi Mazeh: Leuven-Binaries 2212 1.0 MM

2M 1M

Tsevi Mazeh: Leuven-Binaries 231001.0 MM Planet

1MPlanet


Kepler first law:


Kepler second law:


Origin of orbits of both stars

Periastron point

Empty


The Masses of Sirius A & B

– 5th closest star to us: d = 2.63pc– Sirius A is the brightest star in the sky


Wobble of Sirius


Sirius AB Binary System

HST image


Orbits of Sirius A and B



24.7 Vm

0013.01010 9.25.2/24.7

,

,

VA

VB

L

L


• 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:



• 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



1915-Adams obtained a spectrum of Sirius B T~25,000 K

1862- Clark resolved the two stars


%)3(0084.0 SunB RR


The H-R Diagram

L = 4 R2 T4

425 ///107.5 Kscmerg

%)3(0084.0 SunB RR


The Sizes of Stars


Gliese 229B8’’ separation

10 mag difference in J,H,K

(Nakajima 1995)


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

39Tsevi Mazeh: Leuven-Binaries

40

One star with a spectrum composed of two spectra

Tsevi Mazeh: Leuven-Binaries

41

The Doppler Effect

Spectrum of Hydrogen in Lab

Spectrum of a

Star

radv

c


42

Spectroscopic binary

Spectrum of Hydrogen in Lab

Spectrum a Star…..Day 1





43

21 MM

2M 1M

To earthTsevi Mazeh: Leuven-Binaries

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.


45


Double-lined spectroscopic binary.


46




Single-lined spectroscopic binary (SB1)

50

Eclipsing Binaries

Animation Tsevi Mazeh: Leuven-Binaries

http://www.shef.ac.uk/uni/academic/N-Q/phys/people/vdhillon/seminars/sas/eclipsing.html

51

• 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


52

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


53

)()( 1421 TTP

aRR

)()( 2321 TTP

aRR


54

The geometry of the eclipse



Relative dimension: )()( 2321 TTP

aRR

Relative surface flux

Inclination

56

CoRoT-Exo-2


58

Absolute Properties of the Main-Sequence Eclipsing Binary Star BP Vulpeculae


Lacy et al. 2003

59

BP VULPECULAE



BP VULPECULAE

1Tsevi Mazeh: Leuven-Binaries 2 3 Double stars Rev. John Mitchell - 1767 it is highly probable in...

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