Radial velocities amateur measures Exoplanets and double stars - - PowerPoint PPT Presentation
Radial velocities amateur measures Exoplanets and double stars CAPAS 2012 Christian Buil Two objects linked by gravity r m Rotation around commun center of gravity R M Rotation velocity of Sun relative to the Solar system gravity center =
Exoplanets and double stars
CAPAS 2012
Christian Buil
Rotation around commun center of gravity
Rotation velocity of Sun relative to the Solar system gravity center = 13 m/s
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:
Nova Cyg 2001 N°2 FWHM Halpha = 3400 km/s
Doppler effect – Novae example
Measure of gaz ejection velocity
Doppler effect = a dynamic sky…
False color dynamic spectrum of Rigel (β Ori) . Halpha line
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)
Example of spectroscopic double star MIZAR
Access to orbital description
Spectrographe eShel + télescope C11 + caméra CCD QSI-532
Example of MIZAR
2D representation of periodic variations Wavelength Time (pahse)
Halpha detail
Celestron 11 telescope (0.28 m diameter) and eShel spectrograph (suburban Castanet-Tolosan)
Exoplanet catalog (sample !)
(complete list: exoplanet.org)
Classification by radial velocity decrement Exoplanets example
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
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
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 !
3 angströms = 68 km/s
Return to MIZAR spectrum…
The spectral signature of tau Boo b is 150 time inferior !
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 A
Increase the measure precision by a factor 10 is necessary!
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
Many thousand line available on a solar type star
(here eShel spectrograph at R = 10000)
Correlation : 100% Correlation : 90% Correlation : 60% Correlation : 30% THE KEY FOR PRECISION: CROSS-CORRELATION
Measure of correlation degree between observed spectrum (in black) and a reference spectrum (in red)
Cross Correlated Function = CCF Warning, convert the spectra in a linear scale relative to velocity (constant effect of the Doppler along the spectral range).
Some math (log scaling)
Echelle en longueur d’onde Décalage 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) / N avec 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
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
eShel spectrograph : eShel - R = 11000
(Shelyak Instrument)
Example of eShel spectrum
R = resolution power λ = wavelengthl δλ = spectral thickness
(Shelyak Instrument)
Use of eShel spectrograph
No mechanical flexure Controled thermal condition
Caméra CCD QSI-532 (CCD Kodak KAF3200)
Refroidissement aidé par circulation liquide
Remember : tau Boo b semi amplitude is only +/- 460 m/s seulement !
Spectre de l’étoile P Cyg (télescope C11) Spectre d’une lampe d’étalonnage Thorium-Argon
Use of Thorium-Argon lamp for spectral calibration
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)
Acquisition and processing
Repères :
Soleil = 29,8 km/s en moyenne, à corriger.
même = 464 m/s, à corriger.
vitesse de la Terre 1 m/s par minutes de temps).
heures d’observations (alternances étoile / ThAr)
Ecriture d’un programme informatique de traitement automatisé et précis (périodogramme Lomb- Scargle, corrections héliocentrique, CCF, …)
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!
Periodogram tool. Observed period : 3.317 jours. Official value : 3,312 jours. Computer ephemeris
Evaluation of orbit period and phase
Final result
Phase curve of tau Boo system
(error bar is +/- 75 m/s)
Example of HD189733 b extrasolar
Périodogram (two possible period – sampling effect) Phase curve
More easy : HD195019 b
Magnitude 6,9 – Period = 18,2 jours – K = 275 m/s
Barre d’erreur de +/- 50 m/s
More difficult : 51 Peg b (a mythical object !)
Magnitude 5,5 – Period = 4,23 jours – K = 56 m/s
Error bar: +/- 50 m/s
51 Pégase
Michel Mayor, Didier Queloz Septembre 1994 – Septembre 1995 Spectrograph Elodie – 1.93 m telescope Observatoire de Haute-Provence
51 Pégase
Christian Buil 24 juin 2009 – 5 aout 2009 Spectrograph eShel – 0.28 m telescope Observatoire de Castanet-Tolosan
FWHM = spectral line shape S/B = signal to noise ratio W = spectral range wide
Evaluation pour eShel :
(3 sigma error)
Radial velocity measure (RV) : performance function of magnitude and telescope
Simultaneous observation of stellar line and reference calibration line Goal: Limit mechanical flexure induced errors
LHIRES III spectrograph Argon lamp (Filly) Halpha regjon TOWARD HIGH PRECISION RADIAL VELOCITY (NON ECHELLE SPECTROGRAPH)
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 spectrograph 600 l/mm – R = 4000
Near IR observation
The interference fringes problem
High quality flat-field are mandatory
57 Cyg – Télescope de 190 mm, spectrographe R = 3000 (aout 1999)