The orbital elements
description
Transcript of The orbital elements
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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
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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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Single-lined spectroscopic binary (SB1)
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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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Short-period binaries
• Circularization of short-period binaries
• Mass-ratio distribution • Extra-solar planets
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Mazeh et al. 2003
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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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The Cross-Correlation Function
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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The Cross-Correlation Function
Two nicely separated peaks
The two peaks are blended
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The Cross-Correlation Function
• 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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Two-Dimensinal CORrelation - Introduction
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Two-Dimensinal CORrelation - Introduction
),( 21 vvcFunction of two variables
Two main ridges
“Cuts” along the ridges
“)freeze” oneVelocity(
Estimated pair of velocities
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Two-Dimensinal CORrelation - Introduction
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
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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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Short-period binaries
• Circularization of short-period binaries
• Mass-ratio distribution • Extra-solar planets
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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
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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
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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
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Test particle around a star with mass M
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Spectroscopic Binaries
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Single-lined spectroscopic binary (SB1)
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Double-lined spectroscopic binary (SB2)