The orbital elements

Tsevi Mazeh: Leuven-Spectrospic binaries

The precession of the periastron

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

4Tsevi Mazeh: Leuven-Spectrospic binaries

to observer

The shape determines e and

Spectroscopic elements:

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

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

The gravitatonal field )( 21 mmG

Single-lined spectroscopic binary (SB1)

Double-lined spectroscopic binary (SB2)

The relativistic Doppler effect (Margon et al. 1979)

V Systematic surveys

Latham, Mazeh et al. 1992

Short-period binaries

• Circularization of short-period binaries

• Mass-ratio distribution • Extra-solar planets

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

• Circularization• Synchronization• Alignment

Observational evidence

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

• Circularization• Synchronization• Alignment

Observational evidence

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

2001, A&A, 378, 898

Latham et al. 2002

Mazeh et al. 2003

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

[TwO-Dimensional CORrelation]

Shay Zucker & Tsevi Mazeh

The Cross-Correlation Function

Observedspectrum

Templatespectrum

Radial Velocity

Cross-Correlation

nmtmgN

nc )()(1

1)(1 nc

Observed spectrum )(ng

)(ntTemplate

Single-line Spectroscopic Binary

Double-line Spectroscopic Binary

Observedspectrum

Two nicely separated peaks

The two peaks are blended

• Spectral mismatch between secondary and template

• Faint secondary spectrum

• Blended peaks

Two-Dimensional CORrelation - Introduction

)(ngObserved spectrum

)(1 ntPrimary template

)(2 ntSecondary template

Relative weight

Zucker & Mazeh 1994

Two-Dimensinal CORrelation - Introduction

nmtmgN

nc )()(1

)( nmt )()( 2211 nmtnmt

221121

)()();,(

ncncnnc

),( 21 vvcFunction of two variables

Two main ridges

“Cuts” along the ridges

“)freeze” oneVelocity(

Estimated pair of velocities

Freeze the secondary

velocity

Freeze the

primary velocity

Measuring mass ratios of SBs:

q=0.29+/-0.04 01.008.0

Mazeh et al. 2003

The Mass-Ratio Distribution

2-3 measurements

are enough!

G62-61G26-38

Already have primary solution

Just need to constrain the secondary

solution

Mazeh et al. 2003

to observerRad

s m )(

Planet

Sun MMdayiSinMMP

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

HD 114762

Grether & Lineweaver 2006

The Brown-Dwarf Desert

Extrasolar Planets Aug 2012

Jupiter

Neptune

RVGoing smaller

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

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

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

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

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

HD 41004

)Not to scale(!

• A Planet and a Brown Dwarf in the same system

Kepler mission

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

Kepler binaries

Kepler GO 0025

1/3V GM

1/32 GM

Test particle around a star with mass M

Spectroscopic Binaries

Double-lined spectroscopic binary (SB2)

The orbital elements

Documents

Transcript of The orbital elements

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