1. Observational Methods 1.Spectroscopy 2.Photometry Prof. Dr. Artie Hatzes artie@tls-tautenburg.de 036427-863-51 www.tls-tautenburg.de -> Lehre -> Jena

2. Spectroscopic Measurements

3. Observations of oscillations in stars and the sun focus on measuring the velocity field (Doppler measurements) and brightness variations caused by the oscillations. What is the expected amplitude of such variations?

4. Classical Cepheids have brightness variations of few tenths of a magnitude and velocity variations of many km/s

5. Solar-like oscillations have much lower amplitudes because these are not ‚global‘ variations like Cepheids

6. The magnitude of „solar-like“ observations can be estimated using the scaling relationships of Kjeldsen & Bedding (1995) v osc = L/L סּ M/M סּ 23 cm/sec Sunlike stars: 0.2 – 1 m/s Giant stars: 5 – 50 m/s Velocity:

7. The magnitude of „solar-like“ observations can be estimated using the scaling relationships of Kjeldsen & Bedding (1995)  L/L ≈ L/L סּ M/M סּ 4.7 ppm Sunlike stars: 4.7 ppm Giant stars: a few milli-mag Light: ppm = 10 –6

8. Doppler Measurements

9. Measurement of Doppler Shifts In the non-relativistic case: – 0 0 = vv c We measure  v by measuring 

10. collimator Spectrographs slit camera detector corrector From telescope Cross disperser

11. slit camera detector corrector From telescope collimator Without the grating a spectograph is just an imaging camera

12. A spectrograph is just a camera which produces an image of the slit at the detector. The dispersing element produces images as a function of wavelength without disperser with disperser slit fiber

13. 5000 A 4000 A n = –1 5000 A 4000 A n = –2 4000 A 5000 A n = 2 4000 A 5000 A n = 1 Most of light is in n=0

14. bb   The Grating Equation m  = sin  + sin  b 1/  = grooves/mm 

16. Modern echelle gratings are used in high order (m≈100). In this case all the orders are stacked on each other

17. mm+1m+2 m m+1 m+2 Cross-dispersion: dispersing element perpendicular to dispersion of echelle grating m+3 m+4

18. yy ∞ 2 y m-2 m-1 m m+2 m+3   Free Spectral Range  m Grating cross-dispersed echelle spectrographs

19. On a detector we only measure x- and y- positions, there is no information about wavelength. For this we need a calibration source y x

20. Traditional method: Observe your star→ Then your calibration source→

21. CCD detectors only give you x- and y- position. A Doppler shift of spectral lines will appear as  x  x →  →  v How large is  x ?

22. Spectral Resolution d 1 2 Consider two monochromatic beams They will just be resolved when they have a wavelength separation of d Resolving power: d = full width of half maximum of calibration lamp emission lines R = d ← 2 detector pixels

23. R = 50.000 →  = 0.11 Angstroms → 0.055 Angstroms / pixel (2 pixel sampling) @ 5500 Ang. 1 pixel typically 15  m 1 pixel = 0.055 Ang → 0.055 x (310 8 m/s)/5500 Ang → = 3000 m/s per pixel = v  c  v = 1 m/s = 1/1000 pixel → 5 x 10 –7 cm = 50 Å A Cepheid variable would produce Doppler shift of several CCD pixels Solar like oscillations will produce a shift of 1/1000 pixel

24. The Radial Velocity Measurements of  Cep between 1975 and 2005 Up until about 1980 Astronomers were only able to measure the Doppler shift of a star to about a km/s

25. Year Radial Velocity (m/s) Year The Radial Velocity error as a function of year. The reason for the sharp increase in precision around the mid-1980s is the subject of this lecture

26. To get a precise radial velocity meausurement you need: Many spectral lines High resolution High Signal-to-Noise Ratio A Stable wavelength reference A Stable spectrograph

27. Wavelength coverage: Each spectral line gives a measurement of the Doppler shift The more lines, the more accurate the measurement:  Nlines =  1line /√N lines → Need broad wavelength coverage Wavelength coverage is inversely proportional to R:  detector Low resolution High resolution 

28. Noise:  Signal to noise ratio S/N = I/  I For photon statistics:  = √I → S/N = √I I = detected photons

29.  (S/N) –1 Price: S/N  t 2 exposure 14 Exposure factor 1636 144400

30. Obtaining high signal-to-noise ratio for pulsating stars is a problem: Time (min) To detect stellar oscillations you have to sample many parts of the sine wave. If you exposure time is comparable to your pulsation period you will not detect the stellar oscillations!

31. max = M/M סּ (R/R סּ ) 2 √T eff /5777K Frequency of the maximum power is found: 3.05 mHz For stars like the sun, the oscillation period is 5 min → 1 min exposure time For good RV measurement you need S/N = 200 On a 2m telescope with a good spectrograph you can get S/N = 100 (10000 photons) in one hour on a V=10 star → 400.000 photons on a V=6 star in one hour, 6600 photons in one minute (S/N = 80). To get S/N = 200 in one minute will require a 5 m telescope → the study of solar like oscillations in other stars requires 8m class telescopes

32. The Radial Velocity precision depends not only on the properties of the spectrograph but also on the properties of the star. Good RV precision → cool stars of spectral type later than F6 Poor RV precision → cool stars of spectral type earlier than F6 Why?

33. A7 star K0 star Early-type stars have few spectral lines (high effective temperatures) and high rotation rates.

34. Instrumental Shifts Recall that on a spectrograph we only measure a Doppler shift in  x (pixels). This has to be converted into a wavelength to get the radial velocity shift. Instrumental shifts (shifts of the detector and/or optics) can introduce „Doppler shifts“ larger than the ones due to the stellar motion z.B. for TLS spectrograph with R=67.000 our best RV precision is 1.8 m/s → 1.2 x 10 –6 cm → 120 Å

35. Problem: these are not taken at the same time…... Short term shifts of the spectrograph can limit precision to several hunrdreds of m/s

37. Solution 1: Observe your calibration source (Th-Ar) simultaneously to your data: Spectrographs: CORALIE, ELODIE, HARPS Stellar spectrum Thorium-Argon calibration

38. Advantages of simultaneous Th-Ar calibration: Large wavelength coverage (2000 – 3000 Å) Computationally simple Disadvantages of simultaneous Th-Ar calibration: Th-Ar are active devices (need to apply a voltage) Lamps change with time Th-Ar calibration not on the same region of the detector as the stellar spectrum Some contamination that is difficult to model Cannot model the instrumental profile, therefore you have to stablize the spectrograph

39. Th-Ar lamps change with time!

40. The Instrumental Profile What is an instrumental profile (IP): Consider a monochromatic beam of light (delta function) Perfect spectrograph

41. Modelling the Instrumental Profile We do not live in a perfect world: A real spectrograph IP is usually a Gaussian that has a width of 2 detector pixels

42. The IP is not so much the problem as changes in the IP No problem with this IP Or this IP Unless it turns into this Shift of centroid will appear as a velocity shift

43. HARPS: Stabilize the instrumental profile

44. Solution 2: Absorption cell a) Griffin and Griffin: Use the Earth‘s atmosphere:

45. O2O2 6300 Angstroms

46. Filled circles are data taken at McDonald Observatory using the telluric lines at 6300 Ang. Example: The companion to HD 114762 using the telluric method. Best precision is 15–30 m/s

47. Limitations of the telluric technique: Limited wavelength range (≈ 10s Angstroms) Pressure, temperature variations in the Earth‘s atmosphere Winds Line depths of telluric lines vary with air mass Cannot observe a star without telluric lines which is needed in the reduction process.

48. Absorption lines of the star Absorption lines of cellAbsorption lines of star + cell b) Use a „controlled“ absorption cell

49. Campbell & Walker: Hydrogen Fluoride cell: Demonstrated radial velocity precision of 13 m s –1 in 1980!

50. A better idea: Iodine cell (first proposed by Beckers in 1979 for solar studies) Advantages over HF: 1000 Angstroms of coverage Stablized at 50–75 C Short path length (≈ 10 cm) Can model instrumental profile Cell is always sealed and used for >10 years If cell breaks you will not die! Spectrum of iodine

51. Spectrum of star through Iodine cell:

52. Use a high resolution spectrum of iodine to model IP Iodine observed with RV instrument Iodine Observed with a Fourier Transform Spectrometer

53. FTS spectrum rebinned to sampling of RV instrument FTS spectrum convolved with calculated IP Observed I 2

54. WITH TREATMENT OF IP-ASYMMETRIES

55. The iodine cell used at the CES spectrograph at La Silla

57. Photometric Measurements

58. And to remind you what a magnitude is. If two stars have brightness B 1 and B 2, their brightness ratio is: B 1 /B 2 = 2.512  m 5 Magnitudes is a factor of 100 in brightness, larger values of m means fainter stars.

59. Detectors for Photometric Observations 1. Photographic Plates 1.7 o x 2 o Advantages: large area Disadvantages: low quantum efficiency

60. Detectors for Photometric Observations 2. Photomultiplier Tubes Advantages: blue sensitive, fast response Disadvantages: Only one object at a time

61. 2. Photomultiplier Tubes: observations Are reference stars really constant? Transperancy variations (clouds) can affect observations

62. Detectors for Photometric Observations 3. Charge Coupled Devices Advantages: high quantum efficiency, digital data, large number of reference stars, recorded simultaneously Disadvantages: Red sensitive, readout time From wikipedia

63. Get data (star) counts Get sky counts Magnitude = constant –2.5 x log [Σ(data – sky)/(exposure time)] Instrumental magnitude can be converted to real magnitude by looking at standard stars Aperture Photometry

64. Aperture photometry is useless for crowded fields

65. Term: Point Spread Function PSF: Image produced by the instrument + atmosphere = point spread function Camera Atmosphere Most photometric reduction programs require modeling of the PSF

66. Crowded field Photometry: DAOPHOT Computer program developed to obtain accurate photometry of blended images (Stetson 1987, Publications of the Astronomical Society of the Pacific, 99, 191) DAOPHOT software is part of the IRAF (Image Reduction and Analysis Facility) IRAF can be dowloaded from http://iraf.net (Windows, Mac, Intel) or http://star-www.rl.ac.uk/iraf/web/iraf-homepage.html (mostly Linux) In iraf: load packages: noao -> digiphot -> daophot Users manuals: http://www.iac.es/galeria/ncaon/IRAFSoporte/Iraf- Manuals.html

67. 1. Choose several stars as „psf“ stars 2. Fit psf 3. Subtract neighbors 4. Refit PSF 5. Iterate 6. Stop after 2-3 iterations In DAOPHOT modeling of the PSF is done through an iterative process:

69. Original DataData minus stars found in first star list Data minus stars found in second determination of star list

71. Special Techniques: Image Subtraction If you are only interested in changes in the brightness (differential photometry) of an object one can use image subtraction (Alard, Astronomy and Astrophysics Suppl. Ser. 144, 363, 2000) Applications: Nova and Supernova searches Microlensing Transit planet detections

72. Image subtraction: Basic Technique Get a reference image R. This is either a synthetic image (point sources) or a real data frame taken under good seeing conditions (usually your best frame). Find a convolution Kernal, K, that will transform R to fit your observed image, I. Your fit image is R * I where * is the convolution (i.e. smoothing) Solve in a least squares manner the Kernal that will minimize the sum: ([R * K](x i,y i ) – I(x i,y i )) 2  i Kernal is usually taken to be a Gaussian whose width can vary across the frame.

74. some stellar oscillations have periods 5-15 min CCD Read out times 30-120 secs What if you are interested in rapid time variations? E.g. exposure time = 10 secs readout time = 30 secs efficiency = 25% Solution: Window CCD and frame transfer Special Techniques: Frame Transfer

75. Reading out a CCD Parallel registers shift the charge along columns There is one serial register at the end which reads the charge along the final row and records it to a computer A „3-phase CCD“ Columns For last row, shift is done along the row

76. The CCD is first clocked along the parallel register to shift the charge down a column The CCD is then clocked along a serial register to readout the last row of the CCD The process continues until the CCD is fully read out. Figure from O‘Connell‘s lecture notes on detectors

78. Frame Transfer Target Reference Mask Transfer images to masked portion of the CCD. This is fast (msecs) While masked portion is reading out, you expose on unmasked regions Can achieve 100% efficiency Store data Data shifted along columns

79. Sources of Errors Sources of photometric noise: 1. Photon noise: error = √N s (N s = photons from source) Signal to noise ratio = N s / √ N s = √N s rms scatter in brightness = 1/(S/N)

80. Sources of Errors 2. Sky: Sky is bright, adds noise, best not to observe under full moon or in downtown Jena. N data = counts from star N sky = background Error = (N data + N sky ) 1/2 S/N = (N data )/(N data + N sky ) 1/2 rms scatter = 1/(S/N)

81. N data rms N sky = 0 N sky = 10 N sky = 100 N sky = 1000

82. 3. Dark Counts and Readout Noise: Electrons dislodged by thermal noise, typically a few per hour. This can be neglected unless you are looking at very faint sources Sources of Errors Typical CCDs have readout noise counts of 3–11 e –1 (photons) Readout Noise: Noise introduced in reading out the CCD:

83. Sources of Errors 4. Scintillation Noise: Amplitude variations due to Earth‘s atmosphere  ~ [1 + 1.07(kD 2 /4L) 7/6 ] –1 D is the telescope diameter L is the length scale of the atmospheric turbulence

85. For larger telescopes the diameter of the telescope is much larger than the length scale of the turbulence. This reduces the scintillation noise.

86. Light Curves from Tautenburg taken with BEST

87. Saturated bright stars A not-so-nice looking curve from an open cluster

88. CCD Counts t t Saturation Saturation + non- linearity

89. Sources of Errors (less important for Asteroseismology) 4. Atmospheric Extinction Atmospheric Extinction can affect colors of stars and photometric precision of differential photometry since observations are done at different air masses Due to the short time scales of stellar oscillations this is generally not a problem

90. A-star K-star Atmospheric extinction can also affect differential photometry because reference stars are not always the same spectral type. Atmospheric extinction (e.g. Rayleigh scattering) will affect the A star more than the K star because it has more flux at shorter wavelength where the extinction is greater Wavelength