tsevi mazeh: leuven-spectrospic binaries 1 the orbital elements

Tsevi Mazeh: Leuven-Spectrospic binaries

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The orbital elements


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The precession of the periastron


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attributed to the following causes:The correction by 42.98" is 3/2 multiple of classical prediction with PPN parameters [6].

Sources of the precession of perihelion for Mercury

Amount (arcsec/Julian century) Cause

531.63 Gravitational tugs of the other planets

0.0254 Oblateness of the Sun( quadrupole moment)

42.98 [4][5] General relativity

574.64 0.69± Total

574.10 0.65± [3] Observed

attributed to the following causes:The correction by 42.98" is 3/2 multiple of classical prediction with PPN parameters [6].

Precession of the perihelion

http://en.wikipedia.org/wiki/Parameterized_post-Newtonian_formalism

http://en.wikipedia.org/wiki/Tests_of_general_relativity

http://en.wikipedia.org/wiki/Quadrupole_moment




http://en.wikipedia.org/wiki/Parameterized_post-Newtonian_formalism


4Tsevi Mazeh: Leuven-Spectrospic binaries

iv

L

to observer


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The shape determines e and


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Spectroscopic elements:

P The orbital periodK The RV amplitude The argument of periastron e The eccentricity The periastron passage The RV of the system

0T

a,e, , , , 0T iConstants of the motion

The gravitatonal field )( 21 mmG

21

sin2

e

ia

PK


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Single-lined spectroscopic binary (SB1)


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9


10


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Double-lined spectroscopic binary (SB2)


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The relativistic Doppler effect (Margon et al. 1979)


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t

V Systematic surveys


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t

V


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Latham, Mazeh et al. 1992


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Latham, Mazeh et al. 1992


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Short-period binaries

• Circularization of short-period binaries

• Mass-ratio distribution • Extra-solar planets


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Spin and orbital angular momentum exchange in binary star systems. Keppens, R.

1997


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• Circularization• Synchronization• Alignment

Observational evidence


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938 binaries found in LMC by the OGLE project, analyzed by EBAS(Mazeh, Tamuz & North 2006)

• Circularization• Synchronization• Alignment

Observational evidence


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PMS

Melo, C. H. F.; Covino, E.; Alcalá, J. M.; Torres, G.

2001, A&A, 378, 898


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Latham et al. 2002


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Mazeh et al. 2003


TODCOR (and TRICOR):How to derive radial velocities from composite spectra

[TwO-Dimensional CORrelation]

Shay Zucker & Tsevi Mazeh


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The Cross-Correlation Function

Observedspectrum

Templatespectrum

Radial Velocity

Cross-Correlation


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mtg

nmtmgN

nc )()(1

)(

1)(1 nc

Observed spectrum )(ng

)(ntTemplate


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Single-line Spectroscopic Binary

SB1

Double-line Spectroscopic Binary

SB2

Observedspectrum


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Two nicely separated peaks

The two peaks are blended


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• Spectral mismatch between secondary and template

• Faint secondary spectrum

• Blended peaks


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Two-Dimensional CORrelation - Introduction

)(ngObserved spectrum

)(1 ntPrimary template

)(2 ntSecondary template

Relative weight

Zucker & Mazeh 1994


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Two-Dimensinal CORrelation - Introduction

mtg

nmtmgN

nc )()(1

)(

)( nmt )()( 2211 nmtnmt

21212

221121

)(21

)()();,(

nnc

ncncnnc


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),( 21 vvcFunction of two variables

Two main ridges

“Cuts” along the ridges

“)freeze” oneVelocity(

Estimated pair of velocities


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Freeze the secondary

velocity

Freeze the

primary velocity


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2

1

K

Kq

SB1

SB2

Measuring mass ratios of SBs:


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q=0.29+/-0.04 01.008.0

Mazeh et al. 2003


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The Mass-Ratio Distribution

2-3 measurements

are enough!

G62-61G26-38

Already have primary solution

Just need to constrain the secondary

solution


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Mazeh et al. 2003



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iv

L

to observerRad

ial V

eloc

ity

Time

P

K

1-3

2

*3

1

s m )(

203

Jup

Planet

Sun MMdayiSinMMP

K


Test particle (planet) around a star with mass MReflex motion of star


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HD 114762


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Grether & Lineweaver 2006

The Brown-Dwarf Desert

Extrasolar Planets Aug 2012

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Earth

Jupiter

Neptune

RVGoing smaller

~20% of the nearby stars have super-earth planets with periods < 50 d

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HD 41004

• A visual pair – K1V/M2V• Separation ~ 0.5 arc-sec• V-magnitude difference 3.7• Parallax 23 milli-arc-sec• Observed regularly in CORALIE


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HD 41004

days 0002.03298.1 P1

1 s m 250 K

Jupmin,2 25.0 MM

A long-term trend of the residuals

Santos et al. 2002

A B


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HD 41004

days 000081.0328199.1 P1s km 081.0192.6 K

Jupmin,2 19MM

HD41004B

HD41004AA long-term trend

Short-period modulation disappeared

Zucker, Mazeh, Santos, Udry & Mayor 2003

• TODMOR – Two Dimension CorrelationA

BBa


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HD 41004

963 38 daysP 199 60 m sK

2, 2.5min JupM M

Follow-up revealed the orbit of a planet around HD41004A

Zucker, Mazeh, Santos, Udry & Mayor 2004


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HD 41004

B

A


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)Not to scale(!

• A Planet and a Brown Dwarf in the same system



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Kepler mission


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http://astro4.ast.villanova.edu/aprsa/kepler/detached

Kepler binaries


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Kepler GO 0025


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Kepler GO 0025

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V a

23

GM

a

1/3

2

GMa

1/3V GM

1/32 GM

VP


Test particle around a star with mass M

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Spectroscopic Binaries



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Double-lined spectroscopic binary (SB2)

tsevi mazeh: leuven-spectrospic binaries 1 the orbital elements

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