Exoplanets and double stars - shelyak-instruments.com · r R M m Two objects linked by gravity Rotation around commun center of gravity Rotation velocity of Sun relative to the Solar

Radial velocities amateur measuresExoplanets and double stars

CAPAS 2012Christian Buil

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

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°2FWHM Halpha = 3400 km/s

Doppler effect – Novae exampleMeasure 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 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)

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

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

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 AIncrease 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-CORRELATIONMeasure 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’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

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 powerλ = wavelengthlδλ = spectral thickness

eShel spectrograph(Shelyak Instrument)

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 !

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 :

-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, …)

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 bMagnitude 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 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

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

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)

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

Near IR observationThe interference fringes problem

High quality flat-field are mandatory

57 Cyg – Télescope de 190 mm, spectrographe R = 3000 (aout 1999)

Thanks for your attention