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 = 13 m/s

Doppler effect: wavelength variation function of radial velocity of the object (along view direction) Doppler equation: Wavelength shift Radial velocity Light velocity Theoritical wavelength (rest wavelength)

Doppler effect – Novae example Measure of gaz ejection velocity Nova Cyg 2001 N°2 FWHM Halpha = 3400 km/s

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 Time (pahse) Wavelength Halpha detail Celestron 11 telescope (0.28 m diameter) and eShel spectrograph (suburban Castanet-Tolosan)

Exoplanets example Exoplanet catalog (sample !) (complete list: exoplanet.org) Classification by radial velocity decrement

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

Numerical example Consider an observed radial velocity (v sin i) of 0.461 km / seconde ( = 461 meters /second) and H α 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 !

Return to MIZAR spectrum… 3 angströms = 68 km/s 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)

THE KEY FOR PRECISION: CROSS-CORRELATION Measure of correlation degree between observed spectrum (in black) and a reference spectrum (in red) Correlation : 100% Correlation : 90% Correlation : 60% Correlation : 30%

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 Echelle en vitesse (log naturel) Décalage en vitesse non linéaire 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 [ λ 1, λ 2] est l’intervalle spectral analysé, alors A = N / ln( λ 2/ λ 1) et B = -N ln( λ 1) / ln( λ 2/ λ 1) Intervalle en vitesse correspondant à un intervalle de 1 bin = ∆ V = c ln( λ 2/ λ 1) / N avec c = célérité de la lumière = 299792.458 km/s Exemple : λ 1 = 4400 A, λ 2 = 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 eShel interface (limitation of mechanical flexures and thermal drift)

eShel spectrograph : eShel - R = 11000 (Shelyak Instrument) R = resolution power λ = wavelengthl δλ = spectral thickness Example of eShel spectrum

eShel spectrograph (Shelyak Instrument)

Use of eShel spectrograph Caméra CCD QSI-532 No mechanical flexure (CCD Kodak KAF3200) Controled thermal condition Refroidissement aidé par circulation liquide - 1 degré Celsius variation = spectral shift of 300 m/s - 1 mBar pressure variation = spectral shift of 90 m/s Remember : tau Boo b semi amplitude is only +/- 460 m/s seulement !

Use of Thorium-Argon lamp for spectral calibration Spectre de l’étoile P Cyg (télescope C11) Spectre d’une lampe d’étalonnage Thorium-Argon

The telescope (C11 - D = 0.28 m) The precision is inverse of to signal to noise ratio (S/B = SNR) Large telescope welcome ! A = constant function of instrument and spectral type

Acquisition and processing Ecriture d’un programme informatique de traitement automatisé et précis (périodogramme Lomb- Scargle, corrections héliocentrique, CCF, …) 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)

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!

Evaluation of orbit period and phase Periodogram tool. Observed period : 3.317 jours. Official value : 3,312 jours. Computer ephemeris

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 51 Pégase Christian Buil Michel Mayor, Didier Queloz 24 juin 2009 – 5 aout 2009 Septembre 1994 – Septembre 1995 Spectrograph eShel – 0.28 m telescope Spectrograph Elodie – 1.93 m telescope Observatoire de Castanet-Tolosan Observatoire de Haute-Provence

Radial velocity measure (RV) : performance function of magnitude and telescope FWHM = spectral line shape S/B = signal to noise ratio W = spectral range wide Evaluation pour eShel : (3 sigma error)

TOWARD HIGH PRECISION RADIAL VELOCITY (NON ECHELLE SPECTROGRAPH) Simultaneous observation of stellar line and reference calibration line Goal: Limit mechanical flexure induced errors LHIRES III spectrograph Argon lamp (Filly) Halpha regjon

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) Thanks for your attention