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Martin Kürster MPIA

Martin Kürster MPIA. Radial velocity technique. M. Kürster Radial velocity measurements Heraeus-Physikschule, 17 Oct. 2005. Intro: Pros and Cons Radial velocity Spectrographs RV measurement methods

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Martin Kürster MPIA

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  1. Martin Kürster MPIA Radial velocity technique M. Kürster Radial velocity measurements Heraeus-Physikschule, 17 Oct. 2005

  2. Intro: Pros and Cons • Radial velocity • Spectrographs • RV measurement methods • Time variability analysis • Significance of a detection • RV curves, formulae, m sini issue • Lowest planet masses detectable via RVs • Overview of results and present knowledge • Limitations posed by the star Radial velocity technique Contents: M. Kürster Radial velocity measurements Heraeus-Physikschule, 17 Oct. 2005

  3. (1) It works !  So far the most successful method to find extrasolar planets  > 160 exo-planets to date (2) Can determine basic orbital parameters: P , a , e , Tperi ,  and minimum planet mass: m sini Intro: Radial velocity technique Pros:Cons: (1) Indirect method  interpretation ! (2) Limited to late-type stars (F7V-M5V) with sufficient spectral absorption lines (3) Complications due to stellar activity and pulsations (4) Biased towards close-in planets with short orbital periods (5) Minimum planet mass m sini only  uncertainty planet vs. brown dwarf (6) Large numbers of measurements  dedicated telescopes M. Kürster Radial velocity measurements Heraeus-Physikschule, 17 Oct. 2005

  4. Intro: Radial velocity technique General points on ‘’measurement’’ • Requires high measurement precision ~ 1 – 25 m/s • RV measurements can be made for almost any type of star, • but high precision, as required for planet search, • is attained only for • - main sequence stars of spectral types ~ F7V – M5V • - K giants • (2) Differential measurements: • absolute RVs can in principle be determined, • but at a much lower precision for technical reasons • as well as reasons of stellar physics M. Kürster Radial velocity measurements Heraeus-Physikschule, 17 Oct. 2005

  5. (1) Rate of change of distance d from observer to object (2) Velocity component of object along the line of sight vr Radial velocity: Definition Measurement: wavelength change Δλ  stellar absorption lines  high-resolution spectrographs R = Δλ/λ ~ 100 000 M. Kürster Radial velocity measurements Heraeus-Physikschule, 17 Oct. 2005

  6. Radial velocity: Stellar RV reflex motion: star and planet orbit common center of gravitiy M. Kürster Radial velocity measurements Heraeus-Physikschule, 17 Oct. 2005

  7. Spectrographs: (1) Slit Collimator Prism Camera Detector Tel.  (2) Detector Camera Echelle Grating Fibre Collimator X- Disperser Tel.  M. Kürster Radial velocity measurements Heraeus-Physikschule, 17 Oct. 2005

  8. Echelle format: e.g.: HARPS @ ESO 3.6m similar: UVES @ VLT UT2 “Kueyen” R ~ 120 000 R approximately constant over λ range M. Kürster Radial velocity measurements Heraeus-Physikschule, 17 Oct. 2005

  9. RV measurement methods Requirement:Try to detect Jupiter in orbit around the Sun, i.e. an object of 318 Earth masses with an orbital period of 11.9 yr and causing a stellar RV variation of  12.4 m/s [ Comparison: Earth causes a solar RV reflex motion of just  8.8 cm/s ] in high-res. spectrographs Jupiter would cause a shift of the solar spectrum by ± 1/4300 mm (HARPS) ± 1/7000 mm (UVES) • Task: monitor • spectral shifts of about 0.2 m or ~1/100 pixel • over more than a decade • against instrumental instabilities Need a trick ! M. Kürster Radial velocity measurements Heraeus-Physikschule, 17 Oct. 2005

  10. RV measurement methods cont’d: Trick #1:Simultaneous calibration: (a) stabilize spectrograph:  vacuum, temperature control, dampers (b) record an emission line spectrum (usually ThAr) simult- aneously alongside the stellar spectrum  two fibres (c) analysis: determine shifts of spectra by cross-correlation methods and correct for shifts of the ThAr spectrum Trick #2:Self-calibration with a gas-absorption cell: (a) insert a gas absorption cell (usually I2) in the light path; it superimposes its own absorption lines onto the stellar spectrum (b) evacuate, seal and temperature control cell; ensure a saturated molecular I2 atmosphere (c) analysis: model the combined star+I2 spectrum by suitable templates, i.e. pure star and I2 spectra; - higher resolution versions allow the correction of changes in the instrumental profile M. Kürster Radial velocity measurements Heraeus-Physikschule, 17 Oct. 2005

  11. RV measurement methods cont’d: Iodine gas absorption cells M. Kürster Radial velocity measurements Heraeus-Physikschule, 17 Oct. 2005

  12. RV measurement methods cont’d: Summary: Trick #1: stabilize spectrograph or Trick #2: provide a stable calibration reference HARPS with vacuum vessel Iodine cell M. Kürster Radial velocity measurements Heraeus-Physikschule, 17 Oct. 2005

  13. RV measurement methods cont’d: Comparison: simultaneous I2 self-calibration ThAr method method complexity high: vacuum tank etc. low: standard of instrument spectrogtraph efficiency 4-6 x higher (=: 1) depending on instrument long-term stability complicated: excellent: of reference ThAr lamps age I2 cells are sealed demonstrated *) RV precision ~1 m/s 1 – 2 m/s (spectral types F7V – M5V) *) Issues: (1) long-term vs. short-term precsion (2) stellar activity and pulsations M. Kürster Radial velocity measurements Heraeus-Physikschule, 17 Oct. 2005

  14. ESO 3.6m/CAT +CES Data example: the RV time series of the young G0V star  Hor (Kürster et al. (2000), A&A 353, L33) RV semi-amplitude K = 67 m/s orbital period P = 320 d orbital eccentricity e = 0.16 semi-major axis of planet orbit a = 0.92 AU minimum planet mass m sini = 2.28 Mjupiter M. Kürster Radial velocity measurements Heraeus-Physikschule, 17 Oct. 2005

  15. Time variability analysis • Period search / periodogram analysis:… a whole zoo of methods • - very successful method: 2-fitting of sine waves • plot 2 as a function of frequency or period • related method: Lomb-Scargle periodogram, an adaptation of the FFT • - also possible: fitting of Kepler orbits • but often not robust enough for period search when data are • unevenly sampled - too many free parameters M. Kürster Radial velocity measurements Heraeus-Physikschule, 17 Oct. 2005

  16. Time variability analysis cont’d Significance of a period in2-fitting of sine waves • Bootstrap randomization (or simulation): • retain the times and values of the indivdual RV measurements, but shuffle them and create many (1000 – 10000) artificial data sets • for each artificial data set perform the same period (frequency) search as for the original data • the fraction of the artificial data sets that yields a best-fit 2 equal to (or smaller than) that of the original data somewhere in the frequency search range gives the chance probability (false alarm probability) of the original period value M. Kürster Radial velocity measurements Heraeus-Physikschule, 17 Oct. 2005

  17. Keplerian RV curves  = 0o, 45o, … , 315o e = 0, 0.1, … , 0.9999 K =: 1 P =: 1 vo =: 0 Tperi =: 0  = 0o  = 0o  = 45o  = 90o  = 135o  = 180o  = 235o  = 270o  = 315o M. Kürster Radial velocity measurements Heraeus-Physikschule, 17 Oct. 2005

  18. Formulae: M. Kürster Radial velocity measurements Heraeus-Physikschule, 17 Oct. 2005

  19. mp sin i - issue Obs. i • mp sin i : • lower limit to the true planet mass • but also the most probable mass, because i = 90o is the most probable inclination of the orbit M. Kürster Radial velocity measurements Heraeus-Physikschule, 17 Oct. 2005

  20. Lowest planet masses detectable via RVs RV reflex motion of M dwarfs: — high enough to find terrestrial planets Examples: Proxima Centauri M5V, M*= 0.12 M Barnard’s Star M4V, M*= 0.16 M for e = 0 M. Kürster Radial velocity measurements Heraeus-Physikschule, 17 Oct. 2005

  21. 2-planet • model for • Barnard’s • Star • Data from the VLT+UVES VLT UT2 “Kueyen” UVES • circular orbits assumed • parameters: P1 = 36.4 d P2 = 82.6 d • K1 = 2.67 m/s K2 = 2.02 m/s • a1 = 0.117 AU a2 = 0.201 AU • m1sini = 4.07 M m2sini = 4.05 M • would be “terrestrial planets” Not significant ! M. Kürster Radial velocity measurements Heraeus-Physikschule, 17 Oct. 2005

  22. From non-detections: Upper limits to companion masses Barnard's star Method: Add artificial signals to the data and determine their detection probability using bootstrap techniques HZ: Habitable zone AL: Astrometric mass limits (Benedict et al. 1999, HST FGS) m sini : 99% upper limit to m sini m : (99%)2 upper limit to true mass; m 7.088 m sini M. Kürster Radial velocity measurements Heraeus-Physikschule, 17 Oct. 2005

  23. Overview of results and present knowledge Planet discoveries via RVs: # total discovies: 161 # single planet systems: 143 double planet 13 triple planet 4 quadruple planet systems: 1 • Fraction of stars with planets: • late-F to K main seq. stars: • Jupiter-type up to a = 3 AU: • ~5% • (Marcy et al. 2004, ASP Conf. Ser. 321, 3) • (2) M0-M5 main seq. stars: • Jupiter-type up to a = 1 AU: • ~0.46%(0% … 1.27%) • (Endl et al. 2005, ApJ, submitted) • Are low mass stars (<0.5M) not good at making gas giants ? M. Kürster Radial velocity measurements Heraeus-Physikschule, 17 Oct. 2005

  24. Overview of results and present knowledge cont’d Bias towards short-period, close-in planets: hot Jupiters are a genuine class of objects (Mayor) Bias towards high-mass objects: sparse  “Brown dwarf desert” (all surveys) few brown dwarfs found (e.g. Endl, Hatzes et al.) M. Kürster Radial velocity measurements Heraeus-Physikschule, 17 Oct. 2005

  25. Overview of results and present knowledge cont’d Eccentricities distributed as in binary systems (all surveys) Evidence that metal-rich stars form planets more easily (Mayor team and Marcy/Butler team) M. Kürster Radial velocity measurements Heraeus-Physikschule, 17 Oct. 2005

  26. Limitations posed by the star Remember: high enough precision is only attained for spectral types F7V – M5V and K giants However: Late-type stars have convective envelopes  velocity patterns due to convective inhomogeneities and stellar pulsations  magnetic fields cause star spots which deform stellar absorption lines Result: spurious RV signals M. Kürster Radial velocity measurements Heraeus-Physikschule, 17 Oct. 2005

  27. Limiting factors: Convection http://www.astro.lund.se/~dainis “Surface” granulation  convective blueshift Spectral line bisectors Wiggly spectral lines RV shifts of solar spectral lines FeI Cell size ~ 1000 – 2000 km FeII M. Kürster Radial velocity measurements Heraeus-Physikschule, 17 Oct. 2005

  28. . . . convection — rule of thumb estimate: SunM dwarf Contrast (vis.) 16 % 1.1 % RMS velocity σ 2.6 km/s 0.24 km/s Horizontal cell size ~ 1500 km 80 km  Number visible cells ~ 1.7 x 106 ~ 6.5 x 106  RV uncertainty due to random convective motions ~ 2 m/s ~ 0.1 m/s Input values from 3-D RHD models (Ludwig et al. 2002, A&A 395, 99) small ! typical limit for solar-type stars M. Kürster Radial velocity measurements Heraeus-Physikschule, 17 Oct. 2005

  29. Limiting factors: Activity Magnetic fields: suppress convection locally, change spectrum locally — via temperature decrease in spots — via emission from faculae/plage (— and via Zeeman splitting) Very variable: reconfiguration, activity cycles, rotational modulation Magnetic plasma loops (Hα) Spots and faculae Zeeman splitting M. Kürster Radial velocity measurements Heraeus-Physikschule, 17 Oct. 2005

  30. Rotationally broadened absorption line profile disturbed by a star spot . . . activity and rotation Apparent RV signal vs. rotational phase Convection pattern: suppression  relative redshift component Typically, these effects are smaller in M dwarfs than in solar-type stars as convective velocities and radius ( rotational velocity) are one order of magnitude smaller M. Kürster Radial velocity measurements Heraeus-Physikschule, 17 Oct. 2005

  31. RV secular acceleration dvr /dt Barnard's star: 4.5 m/s/yr GJ 1: 3.7 m/s/yr M. Kürster Radial velocity measurements Heraeus-Physikschule, 17 Oct. 2005

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