1. Spectrographs

2. Literature: Astronomical Optics, Daniel Schroeder Astronomical Observations, Gordon Walker Stellar Photospheres, David Gray

3. 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

4. Note: Resolving Power should not be confused with Spectral Resolution Resolution is  and has units of Angstroms. The smaller  the higher the resolution Resolving power is unitless and the larger the resolving power the higher the spectral resolution.

5. R = 15.000  = 0.73 Å R = 100.000  = 0.11 Å R = 500.000  = 0.022 Å

6. Spectral Resolution The resolution depends on the science: 1. Active Galaxies, Quasars, high redshift (faint) objects: R = 500 – 1000 2. Supernova explosions: Expansion velocities of ~ 3000 km/s d / = v/c = 3000/3x10 5 = 0.01 R > 100

7. R = 3.000 R = 30.000 Even for Quasars, you get more informaton with high resolution Quasar absorption lines

8. 35.0000.160100000 60.0000.09130000 100.0000.05310000 140.0000.046000 200.0000.0283000 R  th (Ang) T (K) 3. Thermal Broadening of Spectral lines:

9. 3000001K 1000003G0 1200025F5 375080F0 2000150A0 R1R1 Vsini (km/s)Sp. T. 4. Rotational Broadening: 1 2 pixel resolution, no other broadening

10. 5. Chemical Abundances: Hot Stars: R = 30.000 Cool Stars: R = 60.000 – 100.000 Driven by the need to resolve spectral lines and blends, and to accurately set the continuum.

11. 6 Isotopic shifts: Example: Li 7 : 6707.76 Li 6 : 6707.92 R> 200.000

13. 7 Line shapes (pulsations, spots, convection): R=100.000 –200.000 Driven by the need to detect subtle distortions in the spectral line profiles.

14. Line shapes due to Convection Hot rising cell Cool sinking lane The integrated line profile is distorted. Amplitude of distortions ≈ 10s m/s

15. The convection pattern distorts the line profile. For narrow lines the best way to measure this is with the so-called „line bisector“ which is a measure of the line asymmetry. Spectral Line Bisectors

16. R = 200.000 R > 500.000 Clearly it is easier to measure a bisector at high resolution

17. 8 Stellar Radial Velocities:  RV (m/s) ~ R –3/2 (  ) –1/2  wavelength coverage R  (m/s) 100 000 1 60 000 3 30 000 7 10 000 40 1 000 1200 The Doppler shift of a star due to planetary companions is 1- 100s m/s → you need high resolution spectrographs

18. collimator Spectrographs slit camera detector corrector From telescope Anamorphic magnification: d 1 = collimator diameter d 2 = mirror diameter r = d 1 /d 2

19. slit camera detector corrector From telescope collimator Without the grating a spectrograph is just an imaging camera The spectrograph produces an image of a slit at the detector

20. 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

21. Spectrographs are characterized by their angular dispersion dd   d Dispersing element dd d A =

22. f dldl dd d dldl d = f In collimated light At the detector, one measures a linear dispersion which depends on the focal length of the camera

23. S dd d dldl d = S In a convergent beam

24. Plate Factor P = ( f A ) –1 = ( f ) dd d P = ( S A ) –1 = ( S ) dd d P is in Angstroms/mm P x CCD pixel size = Ang/pixel

25. w h f1f1 d1d1 A D f d2d2   w´w´ h´h´  D = Diameter of telescope d 1 = Diameter of collimator d 2 = Diameter of camera f = Focal length of telescope f 1 = Focal length of collimator f 2 = Focal length of camera A = Dispersing element f2f2

26. w h f1f1 d1d1 A D d2d2 f w´w´ h´h´ f2f2    w = slit width h = slit height Entrance slit subtends an angle  and  ´ on the sky:  = w/f  ´ = h/f Entrance slit subtends an angle  and  ´ on the collimator:  = w/f 1  ´ = h/f 1

27. w ´ = rw(f 2 /f 1 ) = r  DF 2 h ´ = h(f 2 /f 1 ) =  ´ DF 2 F 2 = f 2 /d 1 r = anamorphic magnification due to dispersing element = d 1 /d 2 w ´ = rw(f 2 /f 1 ) = r  f (f 2 /f 1 ) If the telescope and collimator have focal ratio F (= f/D), then f 1 = Fd 1 and f = FD (collimator and telescope always have the same focal ratio) = r  FDf 2 Fd 1

28. w ´ = rw(f 2 /f 1 ) = r  DF 2 This expression is important for matching slit to detector: 2  = r  DF 2 for Nyquist sampling (2 pixel projection of slit). 1 CCD pixel (  ) typically 15 – 20  m Example 1:  = 1 arcsec, D = 2m,  = 15  m => rF 2 = 3.1 Example 2:  = 1 arcsec, D = 4m,  = 15  m => rF 2 = 1.5 Example 3:  = 0.5 arcsec, D = 10m,  = 15  m => rF 2 = 1.2 Example 4:  = 0.1 arcsec, D = 100m,  = 15  m => rF 2 = 0.6

29. 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 Dispersion Transmission gratings are inefficient as most of the light goes into zero (white light) order. Most modern spectrographs use reflection gratings with a blaze angle.

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

31. dd d = m  cos  = sin  + sin  cos  Angular Dispersion: Linear Dispersion: d dx d dd = dd = 1 f cam 1 d  /d dx = f cam d  Angstroms/mm

32. Resolving Power: w ´ = rw(f 2 /f 1 ) = r  DF 2 dx = f 2 dd d  f 2 dd d  r  DF 2 R = /  = A r 1  d1d1 D  = rr A D d1d1 For a given telescope depends only on collimator diameter Recall: F 2 = f 2 /d 1

33. D(m)  (arcsec) d 1 (cm) 2110 4120 10152 100.526 300.577 300.2538 R = 100.000A = 1.7 x 10 –3  is the typical seeing disk of the star

35. Adaptive Optics corrects for the atmospheric motion and allows one to achieve near diffraction limit

36. What if adaptive optics can get us to the diffraction limit? Slit width is set by the diffraction limit:  = D R = r A D d1d1 D = A r d1d1 R d1d1 100000 0.6 cm 1000000 5.8 cm

37. For Peak efficiency the F-ratio (Focal Length / Diameter) of the telescope/collimator should be the same collimator 1/F 1/F 1 F 1 = F F 1 > F 1/F is often called the numerical aperture NA

38. F 1 < F d/1d/1 But R ~ d 1 /  d 1 smaller =>  must be smaller i.e. you must make the slit narrower and this means that starlight is lost on the edges of the slit

39. Normal gratings: ruling 600-1200 grooves/mm Used at low blaze angle (~10-20 degrees) orders m=1-3 Echelle gratings: ruling 32-80 grooves/mm Used at high blaze angle (~65 degrees) orders m=50-120 Both satisfy grating equation for = 5000 A

40.       Grating normal Relation between blaze angle , grating normal, and angles of incidence and diffraction Littrow configuration:  = 0,  =  =  m = 2  sin  A = 2 sin  R = 2d 1 tan  D A increases for increasing blaze angle R2 echelle, tan  = 2,  = 63.4 ○ R4 echelle tan  = 4,  = 76 ○ At blaze peak  +  = 2  m b = 2  sin  cos  b = blaze wavelength

41. These are the instensity distribution of the first 3 orders of a reflection grating

42. 3000 m=3 5000 m=2 40009000 m=1 6000 14000 Schematic: orders separated in the vertical direction for clarity 1200 gr/mm grating 2 1 You want to observe 1 in order m=1, but light 2 at order m=2, where 1 ≠ 2 contaminates your spectra Order blocking filters must be used

43. 4000 m=99 m=100 m=101 5000 9000 14000 Schematic: orders separated in the vertical direction for clarity 79 gr/mm grating 30002000 Need interference filters but why throw away light? In reality:

44. collimator Cross-dispersed Spectrographs slit camera detector corrector From telescope Cross disperser

45. A cross dispersed echelle spectrograph takes this: 4000 m=99 m=100 m=101 5000 9000 14000 30002000 And turns it into this Which can fit nicely on 2-D dectectors Normal dispersion Cross dispersion in the perpendicular direction

46. The Solar spectrum taken through a cross-dispersed echelle spectrograph

47. There are 3 main types of cross dispersing elements used today: 1. Prisms 2. Gratings 3. Grisms (transmission grating + prism)

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

49. Prism cross-dispersed echelle spectrographs yy ∞ –1 y

50. How does the order separation for grisms look like? yy ∞ 2 If gratings go like: And prisms like yy ∞ –1 And a grism is just a prism + grating then the separation should go like the product or yy ∞

51. Cross dispersion yy ∞   · –1 = Increasing wavelength grating prism grism

52. Cross dispersing elements: Pros and Cons Prisms: Pros: Good order spacing in blue Well packed orders (good use of CCD area) Efficient (> 80 %) Good for 2-4 m telescopes Cons: Poor order spacing in red Order crowding Need lots of prisms for large telescopes

53. Cross dispersing elements: Pros and Cons Grating: Pros: Good order spacing in red Only choice for high resolution spectrographs on large (8m) telescopes Cons: Lower efficiency than prisms (60-80%) Inefficient packing of orders

54. Cross dispersing elements: Pros and Cons Grisms: Pros: Good spacing of orders from red to blue Cons: Low efficiency (40%)

55. IF: interference pattern caused by the spacing of grooves BF: interference pattern caused by a single groove

58. For non-zero  (not in Littrow) the blaze function is not as peaked, but the efficiency is less

59. Wavelength Calibration Your detector (normally a charge coupled device) only records an intensity as a function of location on the detector. There is no wavelength information To „wavelength calibrate“ one observes an emission source with tabulated (laboratory) wavelengths for the emission lines Identify the emission lines and determine wavelength as a function of pixel location Fit a polynomial to the wavelength versus pixel and apply this to all observations

60. Wavelength Calibration Observe your star→ Then your calibration source→ Most used lamp: Th-Ar

61. Important Data reduction issues: 1. Blaze function 2. Scattered Light 3. Reflections

62. Scattered light Scattered light is light that is scattered into the interorder spacing of echelle spectrographs. All instruments have scattered light at some level or another. This must be removed in the reduction process. Why? A cross section along rows of the spectrum of the white light source Bias level of CCD

63. To determine the abundance of an element in the stellar spectrum you need to measure the equivalent width w IdId IcIc w = I c – I IcIc d ∫ w I d + I s I c + I s IsIs w = I c + I s – (I +I s ) I c + I s w = I c – I I c + I s Scattered light reduces equivalent width ∫ ∫ d d Width of a perfectly black line of rectangular profile that would remove the same amount of flux I

64. „Picket Fence“ or reflected light for Littrow configuration

65. Spectrum of a White Light Source (Flat Lamp) Picket fence:

66. So you want to build a spectrograph: things to consider Chose R  product – R is determined by the science you want to do –  is determined by your site (i.e. seeing) If you want high resolution you will need a narrow slit, at a bad site this results in light losses Major consideration: Costs, the higher R, the more expensive

67.  normal  Do I need to tilt the grating to make it fit in my room?

68. Reflective or Refractive Camera? Is it fed with a fiber optic? Camera pupil is image of telescope mirror. For reflective camera: Image of Cassegrain hole of Telescope camera detector slit Camera hole Iumination pattern

69. Reflective or Refractive Camera? Is it fed with a fiber optic? Camera pupil is image of telescope mirror. For reflective camera: Image of Cassegrain hole camera detector A fiber scrambles the telescope pupil Camera hole ilIumination pattern

70. Cross-cut of illumination pattern For fiber fed spectrograph a refractive camera is the only intelligent option fiber e.g. HRS Spectrograph on HET: Mirror camera: 60.000 USD Lens camera (choice): 1.000.000 USD Reason: many elements (due to color terms), anti reflection coatings, etc. Lost light due to hole in mirror

71. Stability: Mechanical and Thermal? HARPS HARPS: 2.000.000 Euros Conventional: 500.000 Euros

72. Why spend the money for stability? If you are making precise Doppler measurements of stars (1-10 m/s) the instrumental shifts can be larger than the stellar shifts

73. Tricks to improve efficiency: Overfill the Echelle d1d1 d1d1 R ~ d 1 /  w´ ~  /d 1 For the same resolution you can increase the slit width and increase efficiency by 10-20%

74. Atmospheric Seeing Blurs the Image on Slit slit Lost light R = / d = A r 1  d1d1 D But… You catch more photons, but a wider slit means lower resolution

75. Need to turn this Into this

76. Tricks to improve efficiency: Image slicing The slit or fiber is often smaller than the seeing disk: Image slicers reformat a circular image into a line

77. A modern Image slicer that produces 3 slices

78. After building your spectrograph you then have to debug all the problems!

79. Fourier Transform Spectrometer

80. Interferogram of a monchromatic source: I(  ) = B( )cos(2  n  )

81. Interferogram of a two frequency source: I(  ) = B 1 (  )cos(2  1  ) + B 2 ( 2 )cos(2  2  )

82. Interferogram of a two frequency source: I(  ) =  B i ( i )cos(2  i  ) = B( )cos(2  )d  –∞ +∞ Inteferogram is just the Fourier transform of the brightness versus frequency, i.e spectrum

84. Words of Advice If it is too good to be true it probably isn‘t Lessons learned: 1. „The Phosphorus Stars“ 2. „The Lithium Stars“ 3. „The non-pulsating, pulsating A stars“ „You have to be careful that you do not fool yourself and unfortunately, you are the easiest person to fool“ - Richard Feynman