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Physics for Planet Hunters

Physics for Planet Hunters. Docentföreläsning C. Clément. 1. Hunt for Exoplanets. Planets that are orbiting other stars = Exoplanets According to http://exoplanet.eu 941 planets discovered. Many sophisticated techniques exists (fraction of planets discovered%) Direct imaging (4%)

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Physics for Planet Hunters

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  1. Physics for Planet Hunters Docentföreläsning C. Clément 1

  2. Hunt for Exoplanets Planets that are orbiting other stars = Exoplanets According to http://exoplanet.eu 941 planets discovered. Many sophisticated techniques exists (fraction of planets discovered%) Direct imaging (4%) Doppler shift / Radial velocity (58%) Transit method (34%) Other Methods (4%) planet passes in front of the star=> variation in light 2

  3. Hunt for Exoplanets Planets that are orbiting other stars = Exoplanets According to http://exoplanet.eu 941 planets discovered. Today focus on the following methods Many sophisticated techniques exists Direct imaging (4%) Doppler shift / Radial velocity (58%) Transit method (34%) Other Methods (4%) setup important concepts leading method 3

  4. Direct Imaging 4

  5. Direct Imaging = Detection of a point source image of the exoplanet Reflected light from the parent star (in the visible) Or Through thermal emission (in the infrared) simulation of 1 Jupiter mass planet around Sun like star ISintensity of light from the Star IPintensity of light from the Planet • Depends on the composition of the planet • This ratio is generally very small • 10-9 for Jupiter-Sun • 10-10 for Earth-Sun • Infrared wavelength • Can be large in very favourable cases • eg. 1 Jupiter at 0.2 AU log10(IP/IS) 5

  6. Angular Separation and some Units Let’s put Earth inside the nearest star system Proxima Centauri at is L = 4.243 ly ~4 1013 km * 1 light-year ~ 1013 km 1 Astronomical Unit 1 AU = 150 106 km L = 4 1013 km Proxima Cent. Sun * 1 arcsecond = 1as = 1/3600 degree = 4.84 10-6 rad So even with 0.1 as we could only see the very nearest neighbours of the Sun Jupiter is at 5.2 AU Exoplanets of interest : close to the host star, angular separations 0.1 – 0.5 as “arcseconds” 6

  7. star light Astronomical Seeing • Light is refracted through the atmosphere • Turbulence in the atmosphere • Refraction index is not uniform nor constant • Varies on a spatial scale of r0 • the size “stable patches of air” • 10-20 cm for good conditions • Changing rapidly with time t0~0.01s • The image is moving over t0 if one has a • telescope aperture larger than r0. 7

  8. Point Source Astronomical Seeing Resulting angular resolution cannot be better than 0.3 – 1 as. Point Spread Function PSF(x,y) After Atmospheric turbulence Point Spread Function PSF(x,y) used to describe the response Either use space telescope or adaptive optics After long exposure the seeing disk 8

  9. Adaptive Optics (AO) DM = Deformable Mirror 9

  10. Adaptive Optics (AO), Wavefront Sensor D δθ array of small lenses “lenslets” with same focal distance Each lenslet images object at ∞ Δyis measured with a CCD*. from f and Δyderive deviation δθ from normal path. Measure deformation of the wave front. Compensate for it using eg. deformable mirror Shack–Hartmann wavefront sensor. 10

  11. Provide information about δθ in each region of the aperture on a time scale comparable or better than t0. δθ1 δθ2 δθ3 δθ4 Need to sample the entire aperture of the main mirror each lenslet yields one δθ Need light source bright enough, guiding star or laser Information from CCD is processed in real time (~1kHz) and used to modify a deformable mirror. Compensation is not perfect: depends on nbr. of lenslets and update frequency. 11

  12. Laird Close, CAAO, Steward Observatory Appears as binary with AO off – Two more stars appear With the deformable mirror / adaptative optics => go below the 0.3 as limit from seeing 12

  13. Diffraction Limit in Optical Telescopes λ is the wavelength pinhole First minimum located at θ given by (FK2002 vågrörörelselära och Kvantfysik destructive interference b/w middle and edge of the hole). D Light Intensity Diffraction pattern from a single slit opening Same phenenom in optical system or telescope with aperture D . The smaller the aperture D => the larger the effect of diffraction 13

  14. Diffraction pattern for a point source Airy disk Two close-by point sources Rayleigh criteria: two points can be separated when the angular separation is equal or larger than Airy’s disk: We define Angular resolution of telescope (diffraction limit) this is an angle! 14

  15. Resolution at λ=500 nm Home telescope D=0.2m R=600 mas Hubble space telescope (no seeing) D=2.4 m R=50 mas Very Large Telescope (with adaptive optics) D=8.2 m R=15 mas VLT (in interferometer mode) D=130m R~1 mas (90% loss of light formula above does not apply) James Webb Space Telescope (JWST, in construction) D=6.5 m R~18 mas European-Extremely Large Telescope (E-ELT, approved) D=39.3m R~3mas Without adaptive optics the all ground telescopes would be limited to performance of a 20 cm telescope. 15

  16. Glare • A planet at 1 UA (distance Sun-Earth) in Proxima Centauri system corresponds to 0.76 as • from host star. • So angularly resolvable • But there is another problem, the glare from the star. Constrast depends on star and planet conditions 16

  17. Criteria for direct imaging of a planet • Define planet is imaged: Signal / Noise = S/N >5 • Simple model • Consider diffraction from the star as the only source of background light • Other sources of background light include • Sky background • Scattering from telescope elements (eg. edge of composite mirrors, support structures) • - Adaptive optics halo contribute to the background • Consider the diffraction pattern from a 1D slit (eventhough telescope is 2D…) is the angular separation b/w planet and star Planet observer Star 17

  18. star light I0 is light intensity from the star at θ=0 Is is light intensity from the star at θ we inserted 1D diffraction pattern approximated Signal over noise ratio is Approximate (strict) criteria for planet detection yields 18

  19. Our simple model yields • At high θ easier to see faint light • At low θ planet needs to be a lot brighter • Can increase sensitivity is I0 is smaller • Find a way to reduce the star light • Coronograph example study for JWST (red dwarf star at 13 ly) planet-star separation θ [as] JWST R~18 mas =0.018 as approximately compatible with graph. Also additional algorithms for background subtraction are usually applied. Clampin et al. 2001 JWST white paper http://www.stsci.edu/jwst/doc-archive/white-papers 19

  20. Coronograph • If we can mask the central star we can limit • Scattering from telescope elements (eg. edge of composite mirrors) • - Diffraction light Lyot Stop: removes diffracted star light focal mask Coronograph can remove about 50% of the planet light while 99% of the star light. increase the S/N ratio by a factor ~50. 20

  21. One of the few directly imaged exoplanet systems HR 8799 HR 8799 HR 8799 Composite image from Keck telescope No Coronograph Observed in Infrared WCS facility at Palomar. Image obtained with coronograph System with three planets at 130 ly. HR 8799 is a young star with young hot planets 21

  22. Conclusion Direct Detection About 38 planets found with this method so far (0.5 – 10 Jupiter masses mJ) Extremely challenging, need to detect Easier in infrared and for young and hot planets Higher resolution => look closer to the star Critical to remove stray light and scattering in the telescope, subtraction Remains very challenging even with planned telescopes (JWST and EELT) (eg. Jupiter / Earth) 22

  23. Radial Velocity Doppler Shift Method 23

  24. B barycenter Principles S P B mP mS r = rSB Both the planet and the star orbit the barycenter of the planet-star system Star rotates around B (much smaller movement than the planet) observer 24

  25. B barycenter Principles S P Star moves towards observer light is blue-shifted by Doppler effect B mP mS r = rSB observer 25

  26. B barycenter Principles P S mP mS r = rSB B Star moves away from observer, light is red-shifted observer 26

  27. B barycenter Principles P S mP mS r = rSB B Star moves away from observer, light is red-shifted Use blue shift/ red shift to measure the velocity of the star versus time observer 27

  28. What can we learn about the planet? Extract Periodicity P and star velocity vS(t) Extract Maximum velocity K Assume circular orbit for simplicity. (See M. Perryman for full calculation with general orbits) Full elliptic orbit can also be used, vS(t) is no longer an ellipse. Star periodicity = P 28

  29. What can we learn about the planet? Extract Periodicity P and star velocity vS(t) Extract Maximum velocity K Assume circular orbit for simplicity. (See M. Perryman for full calculation with general orbits) Full elliptic orbit can also be used, vS(t) is no longer an ellipse. Star periodicity = P We can use Kepler’s 3rd law applied to a relative orbit of the planet w.r.t. the star r is the distance star-planet G is gravitation constant mS is the mass of the star We derive r the distance between star and planet from the period 29

  30. What can we learn about the planet? (2) Stable orbit => centrifugal force in equilibrium with Newton’s force Centrifugal force on the planet Newton’s law mP is the mass of the planet vP is the velocity of the planet We derive vP the planet velocity from the star mass and planet-star distance 30

  31. What is the Planet Mass? B barycenter S P B mP mS r = rSB We can relate the planet mass with the star mass We derive the planet mass mP from: star mass and planet and star velocities vP and vS 31

  32. 1) Measure the period of the star radial velocity variations 2) Derive the distance between the star the planet (Kepler’s 3rd law) 3) Derive the velocity of the planet 4) Derive the mass of the planet From radial velocities measurements we can derive the planet mass. (Note: the stellar mass is know from the star luminosity and spectrum) 32

  33. Inclinded Orbit What we did was in the special case when the observer is in the planet-star orbital plane. The radial velocity is entirely towards or away from the observer. In that case we really measure the full radial speed of the star observer 33

  34. Minimum Exoplanet Mass Now the orbital plane is inclined with angle i “inclination” measured w.r.t. plane perpendicular to line of sight. The observed star radial velocity is the projection of actual velocity i observer The observed mass is a minimum planet mass because we do not know the inclination of the orbit. 34

  35. What radial velocities for the stars? B Assume circular orbits here (for complete derivation see M. Perryman Chap2). Star has a circular orbit around the barycenter of the system. rS rS star orbit radius • Circular orbit • uniform motion with constant radial velocity K. We can now derive what radial velocities to expect! Most easily detectable planets with radial velocities have small Periods and large masses! 35

  36. Examples of stellar radial velocities Adpated from: Cumming et al. 1999 Astrophys J 526 890–915 P is the period in year mJ is the mass of Jupiter mE is the mass of Earth mS is the mass of distant star mSun is the mass of distant star First discovered exoplanet. M51Pegasi=1.11MSun Mayor, M. and Queloz, D. (1995). A Jupiter-mass companion to a solar-type star.Nature, 378:355–359. 36

  37. How to we measure the star radial velocity? Doppler shift! When the star is moving towards us, its light is shifted to the blue. When the star is moving away from us, its light is shifted to the red. Star radial velocity about the star–planet barycentre is given by the small, systematic Doppler shift in wavelength of the many absorption lines that make up the star spectrum. 37

  38. Doppler Effect in Classical Physics observer observer source not moving w.r.t. observer source moving w.r.t. observer c velocity of waves in the medium vobs velocity of observator in medium vsource velocity of source in medium λobs observed wavelength λem emitted wavelength see FK2002 vågrörelselära och Kvantfysik. Velocities are measured w.r.t. medium Velocity directions measured w.r.t. an axis eg. connecting source and observed. 38

  39. We are looking at the Doppler shift of the Star, moving away or towards us. • Take observer as reference system • vobs=0 • vsource= vS observed radial velocity vS with relative Doppler shift Special relativistic effects are O(1 m.s-1) and not negligible. 39

  40. Requirements on the spectrograph for Jupiter we havevr~12.5 m.s-1c =3 108m.s-1 thus need to be able to detect ~4 10-8 absorption lines Here an example of a very large Doppler shift obtained with a spectrometer. In the case of star-planets the lines are shifted by one part in 108 ! Distant Galaxy Cluster Sun 40

  41. Echelle Spectrograph Use the diffraction grating at high angle additional path length Δℓ θ i incoming and outgoing wave fronts Difference in path between to rays: Use configuration with An echelle grating i incidence angle θ diffraction angle d distance between two lines The diffraction spectra are located at d 41

  42. The diffraction spectra are located at At high values of the order m, the spectras are essentially superposed but slightly shifted. Coarse grating needed to be able to allow high values of m ( ) If we look at it is diffracted at for gives gives … the spectrum is diffracted over and over in the same direction for each order centered on a slightly different wavelength

  43. order m-1 order m order m+1 superposed We obtain multiple superposition of the spectrum. 43

  44. Remove the superposition with a second grating perpendicular to the first one star light overlaid diffraction orders an echelle grating orders 2nd dispersing element: grating or prism perpendicular to the 1st wavelengths 44

  45. longestλ orders wavelengths shortestλ Raw spectrum from comet LINEAR C/1999 S4 45

  46. Resolving Power Screen/ light detector Interference+diffraction pattern leads to maximum fringes separated by N -2 minima. d Position of the minima on the screen N slits or lines Width of the maximum fringe single slit (same for transmission and reflection grating) • With a grating of N lines (or N slits), N-2 minima b/w two max fringes • the bright fringes become narrower Relative error onxand λmust be the same This gives us the resolving power of the grating 46

  47. Resolving power of the grating Looking back at the grating studied earlier Assume that the grating is 2cm => N=600 47

  48. Example of spectrum with S/N~1 (Queloz 1995) Top line is same as next but S/N=40 Although the S/N is low, there are about 1000 absorption lines that can be matched, each contains information. M(v) model of the expected spectra eg. measured at the beginning of data taking Cross-correlation function Find ε that minimizes this correlation function 48

  49. star light Spectrograph + Camera • Each invidual line “measures” the Doppler shift with a resolution • 1000 absorption lines • Equivalent to measuring the same Doppler shift 1000 times • Increases precision by BUT There could be deformations in the spectrum such that the Model does not fit the data. Idea= superimpose a well know spectrum on top of the star spectrum sealed I2 vapor cell a few cm thick. 49

  50. The measured absorption spectrum • from the star is overlad with • absorption spectrum from I2 • by comparing the measured I2 • absorption lines with those measured • in the lab • Equivalent of the Point Spread Function • for the spectrum. • Can apply the PSF to the Model before • extracting radial velocity. I2 cell temperature controlled Very stable over years. Can be calibrated in the lab with a precision of 1 in 108 Star this procedure allows to reach accuracy of 108 on radial velocity. 50

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