Exoplanets

Radial velocities amateur measures
Exoplanets and double stars
Christian Buil
CAPAS 2012
Two objects linked by gravity
m
r
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
Theoritical wavelength (rest wavelength)
Radial velocity
Light velocity
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
Time (pahse)
2D representation of periodic variations
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 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 !
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
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)
R = resolution power
λ = wavelengthl
δλ = spectral thickness
Example of eShel spectrum
eShel spectrograph
(Shelyak Instrument)
Use of eShel spectrograph
No mechanical flexure
Controled thermal condition
Caméra CCD QSI-532
(CCD Kodak KAF3200)
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)
A = constant function of instrument and spectral type
The precision is inverse of to signal to noise ratio (S/B =
SNR)
Large telescope welcome !
Acquisition and processing
Ecriture d’un programme
informatique de traitement
automatisé et précis
(périodogramme LombScargle, corrections
héliocentrique, CCF, …)
Repères :
-Vitesse de la Terre autour du
Soleil = 29,8 km/s en moyenne, à
corriger.
-Rotation de la Terre sur ellemême = 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
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
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