Image requirements for the detection and caracterisation of Earth-like planets and hot Jupiter s

Transcription

1 Image requirements for the detection and caracterisation of Earth-like planets and hot Jupiter s Alain Chelli Laboratoire d Astrophysique de Grenoble & Jean-Marie Mariotti Center

2 Content The Optical system The long exposure image Sources of noise Direct imaging Differential imaging Requirements for the detection of an Earth-like planet and hot Jupiters

3 The Optical system Extremely Large Telescope (ELT): 30m Adaptive system capable to provide high Strehl ratios (> 0.5) Rotation shearing coronograph Wavefront division Rotation of 180 deg plus π phase shift Cancel the coherent part of the wave

4 Long Exposure Image Impulse response Coronagraphic image Image Dynamics

5 Sources of noise Photon noise & speckle noise of the residual incoherent stellar halo Direct imaging: the variance of the speckle noise is equal to the square of the intensity (Dainty, 1974) Differential imaging: need to evaluate the spatial and spectral correlation coefficient of the speckle noise (Chelli, 2005) Correlation length = ro

6 Direct Imaging: signal and noises Signal Speckle noise Photon noise f : flux ratio between planet and star S : Strehl ratio K : total number of photoevents γ : planet distance to the star γr : planet distance in Airy disk units R : Spectral resolution (λ/δλ) τ : speckle lifetime T : total integration time

7 Direct Imaging: SNR At high Strehl ratios, the SNR is controlled by the dynamics D(γ) The speckle noise is generally much higher than the photon noise: need of differential imaging

8 Differential imaging: the method Consists in making the difference between 2 images simultaneously obtained at 2 wavelenths λ1 and λ2 (properly weighted and rescaled) in order to minimize the differential speckle noise The differential speckle noise is proportional to Δλ/λ. It can easily be decreased at levels below the photon noise.

9 Differential Imaging: useful signal If the distance between the 2 bands is such that: Δλ/δλ > R /γr then the 2 contributions of the planet are fully separated in the image difference γr = 10 R =100 Δλ/δλ = 2 γr = 100

10 Differential Imaging: SNR Signal Speckle noise Photon noise SNR

11 Experimental Parameters Strehl ratio : 0.75 Integration time: 12 heures for an Earth-like planet and 1 hour for a hot Jupiter Speckles lifetime:10 x (λ/0.5)^1.2 ms Overall transmission: 0.2 Differential imaging: _/ = 100 & the combined signal of 10 couples de adjacent bands

12 Requirements for the detection of Earth-like planet and Hot Jupiter with a 30m class telescope SP Distance (m ) Earth:1.5x10-10 (12hours) Dynamics for SNR=5 hot Jupiter:10-6 (1 hour) SNR for Dynamics=10^3 G2V x10^7 85 K0V x10^6 110 K5V x10^6 180 M0V x10^6 280 M5V x10^4 1080

13 Summary To detect an Earth-like planet with a 30m telescope in a 12 hours integration time a dynamics of 10^6 to 10^7 at 0.1 distance is required At present, the best dynamics achieved is a few thousand at 0.5 distance On hot Jutipers, SNR larger than 100 are achieved in 1 hour integration time

14 Constraints on common aberrations Instrumental aberrations induce a noise similar to the speckle noise For the detection of the Earth to be effective, we need to maintain the noise induced by aberrations below the speckle noise after 12 hours integration time, ie:

15 Constraints on common aberrations (2) Assuming: 1 nanometer The constraints on non common aberrations are probably stronger: Simulations