exoplanets and double stars - shelyak-instruments.com · r r m m two objects linked by gravity...
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Radial velocities amateur measuresExoplanets and double stars
CAPAS 2012Christian Buil
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r
R M
m
Two objects linked by gravity
Rotation around commun center of gravity
Rotation velocity of Sun relative to the Solar system gravity center = 13 m/s
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Doppler effect: wavelength variation function of radial velocity of the object (along view direction)
Wavelength shift
Theoritical wavelength (rest wavelength)
Radial velocity
Light velocity
Doppler equation:
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Nova Cyg 2001 N°2FWHM Halpha = 3400 km/s
Doppler effect – Novae exampleMeasure of gaz ejection velocity
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Doppler effect = a dynamic sky…
False color dynamic spectrum of Rigel (β Ori) . Halpha line
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Detection and measure of spectroscopic stars and exoplanet by using Doppler effect
Deux astres tournant autour de leur centre de gravité commun :
If object move to the observers = bleu shift. If object go back = red shift
Technique : measure of star lines position in the spectrum and comparison with rest wavelength (velocimetry)
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Example of spectroscopic double star MIZAR
Access to orbital description
Spectrographe eShel + télescope C11 + caméra CCD QSI-532
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Example of MIZAR2D representation of periodic variations
Wavelength
Tim
e (p
ahse
)
Halpha detail
Celestron 11 telescope (0.28 m diameter) and eShel spectrograph (suburban Castanet-Tolosan)
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Exoplanet catalog (sample !)(complete list: exoplanet.org)
Classification by radial velocity decrement
Exoplanets example
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Apparent measured velocity , Va, is the projection on the sky plane of real velocity, V
Va = V sin i
i = inclinaison of orbital plane
i = 85°i = 60°
i = 0°
Maximal radial velocity
Null radial velocity
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Numerical example
Consider an observed radial velocity (v sin i) of 0.461 km / seconde ( = 461 meters /second)
and Hα line at 6563 angströms.
Compute the spectral shift ?
Doppler formulae:
c = ligth veolocity (celerity) = 300 000 km/s
Answer :
i.e. 1/100 of Angström unit
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Example of tau Bootis system
Minimal request for tau Boo b detection: 0,01 A precision. But for confirm a 5 time better precision is necessary, so 0,01 / 5 = 0,002 angström !
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3 angströms = 68 km/s
Return to MIZAR spectrum…
The spectral signature of tau Boo b is 150 time inferior !
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LHIRES III compatibility ?
Typical resolution power R = 15000
At wavelength λ = 6563 A, FWHM = 0,44 angström ( = 20 km/s)Absolute centroid evaluation on a high contrast line : FWHM / 20 = 0,02 AIncrease the measure precision by a factor 10 is necessary!
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Solution: (1) Observe a large number of lines in the same time(2) Compute the Doppler shift for a large line ensemble (« mean »)
Best situation:(1) Select cool stars i.e. numerous fine lines available (types F, G, K)(2) Observe a wide spectral range (access to bleu spectral domain)(3) Of course, high quality spectral calibration necessary
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Many thousand line available on a solar type star(here eShel spectrograph at R = 10000)
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Correlation : 100%
Correlation : 90%
Correlation : 60%
Correlation : 30%
THE KEY FOR PRECISION: CROSS-CORRELATIONMeasure of correlation degree between observed spectrum (in black) and a reference spectrum (in red)
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Cross Correlated Function = CCF
Warning, convert the spectra in a linear scale relative to velocity (constant effect of the Doppler along the spectral range).
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Some math (log scaling)
Echelle en longueur d’ondeDécalage en vitesse non linéaire
Echelle en vitesse (log naturel)Décalage en vitesse linéaire
n = A x ln(λ) + B = rang du bin dans le spectre linéarisé
Si N est le nombre de bin total choisi et si [λ1, λ2] est l’intervalle spectral analysé, alors
A = N / ln(λ2/λ1) et B = -N ln(λ1) / ln(λ2/λ1)
Intervalle en vitesse correspondant à un intervalle de 1 bin = ∆V = c ln(λ2/λ1) / Navec c = célérité de la lumière = 299792.458 km/s
Exemple : λ1 = 4400 A, λ2 = 6445 A, N = 32767 -> A = 85845, B = -720194 et ∆V = 3,49 km/s
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How to access to a wide spectral range ?
Use of an échelle spectrograph
How to calibrate ?
Use optical fibers link between telescope and spectrograph
(limitation of mechanical flexures and thermal drift)
eShel interface
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eShel spectrograph :eShel - R = 11000
(Shelyak Instrument)
Example of eShel spectrum
R = resolution powerλ = wavelengthlδλ = spectral thickness
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eShel spectrograph(Shelyak Instrument)
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Use of eShel spectrograph
No mechanical flexureControled thermal condition
- 1 degré Celsius variation = spectral shift of 300 m/s- 1 mBar pressure variation = spectral shift of 90 m/s
Caméra CCD QSI-532(CCD Kodak KAF3200)Refroidissement aidé par circulation liquide
Remember : tau Boo b semi amplitude is only +/- 460 m/s seulement !
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Spectre de l’étoile P Cyg (télescope C11)
Spectre d’une lampe d’étalonnage Thorium-Argon
Use of Thorium-Argon lamp for spectral calibration
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The precision is inverse of to signal to noise ratio (S/B = SNR)Large telescope welcome !
A = constant function of instrument and spectral type
The telescope (C11 - D = 0.28 m)
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Acquisition and processing
Repères :
-Vitesse de la Terre autour du Soleil = 29,8 km/s en moyenne, à corriger.-Rotation de la Terre sur elle-même = 464 m/s, à corriger.-Mesure du temps (variation de la vitesse de la Terre 1 m/s par minutes de temps).-Un point de mesure représente 2 heures d’observations (alternances étoile / ThAr)
Ecriture d’un programme informatique de traitement automatisé et précis(périodogramme Lomb-Scargle, corrections héliocentrique, CCF, …)
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Detection of tau Boo b
Localisation de tau Boo dans le ciel
Black dots: measured radial velocity radiale mesurée en fonction du temps (points noirs)(Red plot: theoritical ephemeris, 3,312 jours period)
The total amplitude of spectral shift represent 1/100 of pixel size!
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Periodogram tool. Observed period : 3.317 jours. Official value : 3,312 jours.
Computer ephemeris
Evaluation of orbit period and phase
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Final result
Phase curve of tau Boo system(error bar is +/- 75 m/s)
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Example of HD189733 b extrasolar
Périodogram (two possible period – sampling effect)
Phase curve
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More easy : HD195019 bMagnitude 6,9 – Period = 18,2 jours – K = 275 m/s
Barre d’erreur de +/- 50 m/s
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More difficult : 51 Peg b (a mythical object !)Magnitude 5,5 – Period = 4,23 jours – K = 56 m/s
Error bar: +/- 50 m/s
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51 PégaseMichel Mayor, Didier Queloz
Septembre 1994 – Septembre 1995Spectrograph Elodie – 1.93 m telescope
Observatoire de Haute-Provence
51 PégaseChristian Buil
24 juin 2009 – 5 aout 2009Spectrograph eShel – 0.28 m telescope
Observatoire de Castanet-Tolosan
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FWHM = spectral line shapeS/B = signal to noise ratioW = spectral range wide
Evaluation pour eShel :
(3 sigma error)
Radial velocity measure (RV) : performance function of magnitude and telescope
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Simultaneous observation of stellar line and reference calibration line
Goal: Limit mechanical flexure induced errors
LHIRES III spectrographArgon lamp (Filly)Halpha regjon
TOWARD HIGH PRECISION RADIAL VELOCITY (NON ECHELLE SPECTROGRAPH)
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Another approach: simultaneous observation of stellar lines and telluric lines
Observation of CaII near IR triplet)
Selected domain for Gaia mission RVS spectrograph(8470 – 8740 A, R = 11000)
LHIRES III spectrograph600 l/mm – R = 4000
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Near IR observationThe interference fringes problem
High quality flat-field are mandatory
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57 Cyg – Télescope de 190 mm, spectrographe R = 3000 (aout 1999)
Thanks for your attention