Observational methods for astrophysics. Pierre Hily-Blant

Transcription

1 Observational methods for astrophysics Pierre Hily-Blant IPAG OSUG-D/ P. Hily-Blant (Master2 APP) Observational methods / 323

2 VI Spectroscopy Lecture VI Spectroscopy P. Hily-Blant (Master2 APP) Observational methods / 323

3 VI Spectroscopy 1. Introduction VI Spectroscopy Introduction Visible/IR mm-astronomy P. Hily-Blant (Master2 APP) Observational methods / 323

4 VI Spectroscopy 1. Introduction Introduction Power spectrum or power spectral density = energy distribution per unit frequency (or wavelength) Spectroscopy: methods to measure the power spectrum of a signal Atoms and molecules identification Physical and chemical conditions of gas and dust Magnetic field strength measurements (Zeeman effect) Precise redshift measurement Exoplanets (radial velocities, multi-band transits) P. Hily-Blant (Master2 APP) Observational methods / 323

5 VI Spectroscopy 1. Introduction Lines P. Hily-Blant (Master2 APP) Observational methods / 323

6 VI Spectroscopy 1. Introduction Lines P. Hily-Blant (Master2 APP) Observational methods / 323

7 VI Spectroscopy 1. Introduction Spectral information Intensity Position Profile or shape Polarization P. Hily-Blant (Master2 APP) Observational methods / 323

8 VI Spectroscopy 1. Introduction Spectral information P. Hily-Blant (Master2 APP) Observational methods / 323

9 VI Spectroscopy 1. Introduction Spectral information P. Hily-Blant (Master2 APP) Observational methods / 323

10 VI Spectroscopy 1. Introduction Spectral information P. Hily-Blant (Master2 APP) Observational methods / 323

11 VI Spectroscopy 1. Introduction Gas Velocity field in clouds Rotational lines towards prestellar cores Line velocity, line width, line shape P. Hily-Blant (Master2 APP) Observational methods / 323

12 VI Spectroscopy 1. Introduction Gas Velocity field in clouds Maps of spectra CO(1-0) rotational line mapped towards a molecular cloud P. Hily-Blant (Master2 APP) Observational methods / 323

13 VI Spectroscopy 1. Introduction Gas Velocity field in clouds Maps of spectra CO(1-0) rotational line mapped towards a molecular cloud P. Hily-Blant (Master2 APP) Observational methods / 323

14 VI Spectroscopy 1. Introduction Gas Velocity field in clouds Maps of spectra CO(1-0) rotational line mapped towards a molecular cloud P. Hily-Blant (Master2 APP) Observational methods / 323

15 VI Spectroscopy 1. Introduction Spectrometers: general characteristics Analogic or digital Figures of merit: central frequency: ν 0 spectral resolution δν resolution power R = ν 0 /δν = λ 0 /δλ Frequency calibration (ν 0, δν) is involved P. Hily-Blant (Master2 APP) Observational methods / 323

16 VI Spectroscopy 1. Introduction Spectrometers: general characteristics Transfer (or instrumental) function P(ν) I (ν) = I 0 (ν) P(ν) P. Hily-Blant (Master2 APP) Observational methods / 323

17 VI Spectroscopy 1. Introduction Doppler effect First order, non relativistic (v/c 1) Convention: v positive for redshifted (δλ > 0) signal δv/c = δν/ν 0 = δλ/λ 0 δv/c = R P. Hily-Blant (Master2 APP) Observational methods / 323

18 VI Spectroscopy 2. Visible/IR VI Spectroscopy Introduction Visible/IR mm-astronomy P. Hily-Blant (Master2 APP) Observational methods / 323

19 VI Spectroscopy 2. Visible/IR Spectrometers: general characteristics Different dispersion type: refraction: prism diffraction: grating both: grism, i.e. grating on a prism narrow-band imaging interferometry Different geometry: slit (long, multi) aperture or multi-fiber Integral field unit (IFU): lenslets or fiber bundles λ-selective imager (Fabry-Pérot) P. Hily-Blant (Master2 APP) Observational methods / 323

20 VI Spectroscopy 2. Visible/IR Spectrometers: general categories Power spectrum Interference: thin plate filters, gratings, slits, Michelson, Fabry-Pérot; from far-ir to X-ray Electrical filters Digital (autocorrelators or FT) Receiver selectivity (e.g. X-ray or γ-ray) Modes sequential: channel by channel (e.g. rotating grating on single detectot; Fabry-Pérot) multichannel: e.g. grating + CCD spectro-imaging: add spatial information (F-P, long-slit, integral-field spectroscopy) P. Hily-Blant (Master2 APP) Observational methods / 323

21 VI Spectroscopy 2. Visible/IR Spectroscopy of visible light light dispersion: refraction: prism diffraction: grating both: grism narrow band interference filters (Hα, [OIII], [SII]): do not provide the line shape Throughput constraints: A T Ω rmsou = A spec Ω spec (= λ 2 at radiofrequencies, because of coherent detection) P. Hily-Blant (Master2 APP) Observational methods / 323

22 VI Spectroscopy 2. Visible/IR Prism spectrograph (historical) n(λ) sin(γ/2) = sin[(δ min + γ)/2] γ: prism angle; δ min : minimum deviation at the minimum deviation incidence, δ only depends on γ and n(λ); angular dispersion: dδ min / dλ = b/h dn/ dλ (rad λ 1 ) δ min = λ/h; R = h δ min / λ = b dn/ dλ b = 100 mm, Hα, dn/ dλ nm 1 or R caveat: all the intensity in the first order P. Hily-Blant (Master2 APP) Observational methods / 323

23 VI Spectroscopy 2. Visible/IR Grating spectrograph Reflecting diffraction grating spectrograph Condition for constructive interference: grating equation (order m): p = sin θ 0 + sin θ = mλ/d θ 0 : incidence angle; θ: diffraction angle; note that sin θ 1 restricts {m, N} P. Hily-Blant (Master2 APP) Observational methods / 323

24 VI Spectroscopy 2. Visible/IR Grating spectrograph Reflecting diffraction grating spectrograph m = pd/λ; s: slit width Normalized intensity: I (p)/i (0) = ( sin πsp/λ πsp/λ )2 sin Nπdp/λ ( Nπdp/λ )2 P. Hily-Blant (Master2 APP) Observational methods / 323

25 VI Spectroscopy 2. Visible/IR Grating spectrograph Reflecting diffraction grating spectrograph Analogy with intensity interferometer: total baseline Nd defines the angular width of each peak; distance between peaks (free spectral interval) set by the size of each slit s P. Hily-Blant (Master2 APP) Observational methods / 323

26 VI Spectroscopy 2. Visible/IR Grating spectrograph Usual setup P. Hily-Blant (Master2 APP) Observational methods / 323

27 VI Spectroscopy 2. Visible/IR Grating spectrograph Grating spectrograph: in practice slit: ensures constant seeing disk size and constant spectral resolution collimator: transforms the divergent light bundle behind the primary focus into a parallel wavefront; β = arcsin(nλ/d sin α) the parallel wavefront illuminates the grating the diffracted light is focused by the camera onto the focal plane Spectral resolution depends on all diffracting elements: point source / atmosphere (seeing) / telescope diffraction (slit) / collimator diffraction / overall grating diffraction / camera diffraction / pixel size P. Hily-Blant (Master2 APP) Observational methods / 323

28 VI Spectroscopy 2. Visible/IR Grating spectrograph Spectral resolution R max = mn Maximum resolving power: fixed by diffraction of the total length of the grating L = Nd, i.e. the max. # of illuminated lines P. Hily-Blant (Master2 APP) Observational methods / 323

29 VI Spectroscopy 2. Visible/IR Grating spectrograph Blazed grating θ = (i i )/2, i θ = i + θ blazing condition: mλ B = 2d sin θ cos(i θ) P. Hily-Blant (Master2 APP) Observational methods / 323

30 VI Spectroscopy 2. Visible/IR Grating spectrograph Blazed grating blazing: high efficiency into a specific diffraction order constructive order m coincides with specular reflection from blazed faces shape of the periodic structure (triangle, wavelike, square) one blaze λ associated with one order blaze conditions: grating characteristics + illumination conditions P. Hily-Blant (Master2 APP) Observational methods / 323

31 VI Spectroscopy 2. Visible/IR Grating spectrograph Grating: spectral resolution R max = mn Maximum resolving power: fixed by diffraction of the total length of the grating L = Nd, i.e. the max. # of illuminated lines square grating, 5cm, 40 grooves per mm (a = 25µm), λ B = 430nm; incidence i = 60 N = 2000, t = 21.6µm, m = 2t/λ B = 100, R = P. Hily-Blant (Master2 APP) Observational methods / 323

32 VI Spectroscopy 2. Visible/IR Grating spectrograph Echelle grating high-order (UVES at VLT: m > 80) long period: a λ; mλ B = 2d sin i = 2t R = 2 tan θ B f coll /L slit ; R up to 10 5 free spectral interval: (m + 1)λ = m(λ + λ) pre-disperser (prism: grism) P. Hily-Blant (Master2 APP) Observational methods / 323

33 VI Spectroscopy 2. Visible/IR Grating spectrograph Sampling considerations P. Hily-Blant (Master2 APP) Observational methods / 323

34 VI Spectroscopy 2. Visible/IR Grating spectrograph Sampling considerations P. Hily-Blant (Master2 APP) Observational methods / 323

35 VI Spectroscopy 2. Visible/IR Grating spectrograph Sampling considerations How many CCD-pixels per line FWHM? Answer: Nyquist oversampling > 2 pixels / FWHM Oversampling required (limited nb of measurements) FWHM =? convolution of instrumental FWHM + line FWHM HARPS (ESO/3.6m): 4.1px/FWHM Interpolation scheme between sampling points also matters (linear, spline) P. Hily-Blant (Master2 APP) Observational methods / 323

36 VI Spectroscopy 2. Visible/IR Grating spectrograph Spectral resolution Diffraction Slit Sensitivity (limit magnitude / overall quantum efficiency / throughput) Grating and blazing CCD pixel size P. Hily-Blant (Master2 APP) Observational methods / 323

37 VI Spectroscopy 2. Visible/IR Grating spectrograph Visible/IR Spectrometers: general categories P. Hily-Blant (Master2 APP) Observational methods / 323

38 VI Spectroscopy 2. Visible/IR Grating spectrograph Visible/IR Spectrometers: general categories P. Hily-Blant (Master2 APP) Observational methods / 323

39 VI Spectroscopy 2. Visible/IR Grating spectrograph Visible/IR Spectrometers: general categories P. Hily-Blant (Master2 APP) Observational methods / 323

40 VI Spectroscopy 2. Visible/IR Grating spectrograph Visible/IR Spectrometers Scanning/F-P: large étendue hence large FOV; Ω 2π/R β/2r for slits (β 0.1rad); R = nf nn P. Hily-Blant (Master2 APP) Observational methods / 323

41 Scanning/Fourier Transform Spectrometer (FTS); requires FT of the OPD-scanning; R = 2OPD max /λ; multiplexing high SNR and improved inter-calibration. P. Hily-Blant (Master2 APP) Observational methods / 323 VI Spectroscopy 2. Visible/IR Grating spectrograph Visible/IR Spectrometers

42 VI Spectroscopy 2. Visible/IR Grating spectrograph Visible/IR Spectrometers IFS/Mirror slicer concept: small mirrors second set of mirrors long-slit spectrograph; P. Hily-Blant (Master2 APP) Observational methods / 323

43 VI Spectroscopy 2. Visible/IR Grating spectrograph Visible/IR Spectrometers IFS/Lenslet concept: P. Hily-Blant (Master2 APP) Observational methods / 323

44 VI Spectroscopy 2. Visible/IR Grating spectrograph Visible/IR Spectrometers Fiber concept: fiber bundle in focal plane long-slit spectrograph; adding lenslets increases filling factor in f-plane. P. Hily-Blant (Master2 APP) Observational methods / 323

45 VI Spectroscopy 2. Visible/IR Grating spectrograph Visible/IR Spectrometers Degradation of throughput in IFU P. Hily-Blant (Master2 APP) Observational methods / 323

46 VI Spectroscopy 2. Visible/IR Grating spectrograph Eisenhauer & Raab (2015) P. Hily-Blant (Master2 APP) Observational methods / 323

47 VI Spectroscopy 3. mm-astronomy VI Spectroscopy Introduction Visible/IR mm-astronomy P. Hily-Blant (Master2 APP) Observational methods / 323

48 VI Spectroscopy 3. mm-astronomy Spectrometers Determine the spectral distribution of the flux Implicitly, with spectral resolution better than few GHz Formerly analogic spectrometers: AOS, filter banks Nowdays, digitial backends: autocorrelators correlators (interferometry, and also polarization with S-D) fast fourier transform Astronomical requirements: bandwidth, channel spacing, polarimetry Technical: low noise, linear Figures of merit: linearity, dynamic range, temporal stability Concerns: cheap, size, power consumption P. Hily-Blant (Master2 APP) Observational methods / 323

49 VI Spectroscopy 3. mm-astronomy Wiener-Khinchine R(τ) = V (t)v (t + τ) dτ S(ν) = R(τ) exp( 2iπντ) dτ W-K theorem: ensures this is true even for stationary time series P. Hily-Blant (Master2 APP) Observational methods / 323

50 VI Spectroscopy 3. mm-astronomy Autocorrelators Sample the incoming voltage at intervals δt during t Compute the autocorrelation (AC) product of the voltage Finally compute a single FFT of the accumalated AC functions Advantages: highly versatile (combinations of δν, ν) can be used as correlators: polarimetry high dynamic range P. Hily-Blant (Master2 APP) Observational methods / 323

51 VI Spectroscopy 3. mm-astronomy Fast Fourier Transform Sample the incoming voltage at intervals δt during t (apodization) Compute real-time FFT of the voltage signal using FPGA squaring: compute the power spectrum Repeat the operation and average the FFT Advantages: CHEAP! 5000 euros/ghz: allow multi-feed arrays easier long-term maintenance (less hardware components) Disadvantage: less versatile than AC becoming very popular: IRAM/30m, APEX P. Hily-Blant (Master2 APP) Observational methods / 323

52 VI Spectroscopy 3. mm-astronomy Bandwidth/resolution instantaneous bandwidth sampling: δt = 1/(2 ν) Total time spectral resolution: δν 1/(2 t) Constraints Number of channels: N = t/δt = ν/δν Signal digitization (1-2 bits): loss of sensitivity Finite t leads to apodization in the spectral domain: final resolution > channel separation P. Hily-Blant (Master2 APP) Observational methods / 323