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天文觀測 I

天文觀測 I. Astronomical Measurements Optical Band. Magnitude. 星等 (magnitude). 即便是現在，天文學家 ( 可見光與紅外 ) 仍以星等表示天體亮度。 星等 西元前二世紀時，希臘天文學家希帕可斯 (Hipparchus) 就把星星們分成六個等級 。 一等星最亮，六等星 ( 肉眼極限 ) 最暗 事實上，所謂之肉眼極限 6 星等是指以肉眼全視野而言，眼睛的靈敏度會受其它地方來的星光所影響。 18 世紀初 , H. Curits and H Russel 發現用準直儀 (collimator)

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天文觀測 I

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  1. 天文觀測 I Astronomical Measurements Optical Band

  2. Magnitude

  3. 星等(magnitude) • 即便是現在，天文學家(可見光與紅外)仍以星等表示天體亮度。 • 星等 • 西元前二世紀時，希臘天文學家希帕可斯(Hipparchus)就把星星們分成六個等級。 • 一等星最亮，六等星(肉眼極限)最暗 • 事實上，所謂之肉眼極限6星等是指以肉眼全視野而言，眼睛的靈敏度會受其它地方來的星光所影響。 • 18世紀初, H. Curits and H Russel 發現用準直儀 (collimator) • 將視野(FOV)拘限在 ~ 5 arcmin • Limiting magnitude +8.5, • 相當於 ~200 photons/s

  4. 星等—定量 • 19世紀，使用儀器來測量星光 • 發現原先所稱一等星的星光強度大約是六等星的100倍 • 當初星等是由肉眼定義出來 • 如聽覺一般，其反應是log scale • Log scale: • 量小時對變化很敏感，增加靈敏度，量大時反應增加得很慢，以保護器官。 • 因此，五星等比六星等亮X倍，四星等比六星等亮X2倍……一星等比六星等亮X5倍

  5. 視星等與flux • 所以星等與 flux (energy per unit time per unit area)可寫做 • 但是，標準為何? • 以哪一顆星為標準

  6. 星等的標準 • 定義:對所有濾鏡系統而言，織女星(Vega)的星等一定是零星等。 • 濾鏡系統：如 UBVRI, 或新出的Sloan g’,r’,I’,z’ • 唯一例外bolometric magnitude • 幾個星等的例子

  7. 定星等 • 原則上，我們只要比較觀測目標與織女星的flux差幾倍，就可得之星等。 • 原則如此，實際操作有困難 • 我們的大氣會對星光產生吸收，不同厚度大氣吸收程度不同，就算是恆星，到望遠鏡的flux也不一樣。 • 如天體在接近天頂與地平線比較，接近地平線時光經過較厚的大氣。 • 因此，以上星等的定義要定義在大氣層之上 • 也就是f為大氣層之上的flux • 此外，目標星與織女星可能相距很遠…… • 二個方向上的大氣狀態可能很不同

  8. Air Mass θ Atmosphere z F(z,0) F(z,θ)

  9. 標準星 • 在實際應用上單一顆織女星是不夠的。 • 因此，有天文學家製作標準星表。 • 如藍道星表（Landolt Catalog）（Landolt, 1992) • 可能的做法 • 先校正出織女星附近恆星的星等，變成標準星 • 再由上述的標準星逐步向外擴張製做出更多的標準星 • 但這些標準星仍然不足 • 通常望遠鏡的視野都很小，LOT:13’x13’，其視野裡大部分的情況是沒有標準星的。 • 那怎麼辦?

  10. Colors

  11. 顏色(color)與濾鏡(filter) • 上面所講述的星等，多半是定義在某一特殊的濾鏡之下。 • 不用濾鏡(稱之白光white light)的觀測也有，較少見。 • 因此星等的定義通常寫為 • 此處的並非波長，而是波段，如V band : mV

  12. 波段 • 為何需要看不同波段? • 可見光波段雖窄，但不同的天體所發的光波長分佈大不相同，有些短波長強些(偏藍)，有些長波長強些(偏紅)。 • 原則上可用光譜來解析，但光譜製作不易(需要大的望遠鏡) • 用不同濾鏡可粗略得知其波長的分佈，而得到天體的某些訊息，如溫度。 • 一般恆星輻射大致像一個黑體輻射 • 不同顏色得輻射可能代表天體不同部分的輻射。 • 吸積雙星:吸積盤- 短波長，伴星:長波長

  13. 顏色、黑體輻射與溫度

  14. 色指數(color index) • The stellar color index is defined by the magnitude difference of the two wavelength bands (usually neighboring bands).  • For example, mB -mV=B-V • The most important color index is B-V, the second one is U-B  • By definition, the color index of Vega is 0. • A star redder than Vega has positive color index. • A star bluer than the Vega has negative color index. • The Sun’s color index: B-V= 0.63, which is redder than Vega.

  15. 色指數與溫度 • The black body is a very good approximation to describe the radiation of a star. The color is also an index for stellar temperature. • Higher temperature  shorter  bluer. • Lower temperature  longer  redder  • Large color index  redder  cooler  • Smaller color index  bluer  hotter.

  16. 赫羅圖H-R Diagram

  17. 恆星分類(光譜型) • The astronomers used to use the strength of these lines to classify the spectra type of the stars • The one with the strongest Balmer absorption lines called A stars • The one with the second strongest Balmer absorption lines called B stars • Etc. • Balmer lines: For H atom transfer from (to) level n>2 to (from) n=2. The lines basically in visible light wavelength • However, if we rearrange these classes of stars by their color (B-V), the O stars are the bluest and then B, A …. • Spectral type ordered in sequence of decreasing effective temperature (increasing the color index): OBAFGKM(RNS) • Oh, Be A Find Girl (Guy), Kiss Me ! (Right Now! Smack) • Each of the main class is further broken down into up 10 subdivision, indicated by the number of 0 to 9 (e.g. A0, G2, K5) • Our Sun is G2 • Vega is A0

  18. 恆星分類(光譜型)

  19. 赫羅圖H-R Diagram

  20. 濾鏡(filters)– Johnson-Cousins (UVBRI)

  21. 濾鏡(filters)– Johnson-Cousins (UVBRI)

  22. 濾鏡(filters)– SDSS (Sloan) System • Wavelength cutoff is very sharp

  23. 二米望遠鏡的儀器 -- 四色同步成像儀 2014/10/4 23

  24. 濾鏡(filters)– Narrow band • For specified emission: like H, OII, OIII

  25. Photometry

  26. Differential Photometry Comparison • Ft = target flux, measured by observation (image) • Fc = comparison star flux, measured by observation (image) • If the apparent magnitude of the comparison is known  The apparent magnitude of target can be obtained. Target

  27. Finding Chart • Note: Once your telescope point to the target. You must compare your image with the finding chart to make sure that you are observing the right source. Target (outburst!!!) Finding Chart LOT image

  28. Comparison Stars Comparison stars Target

  29. Differential Photometry • The star in the FOV is qualified as a comparison star in the FOV if and only if its magnitude is stable. • Usually, we do not choose one but a set of comparison stars. The differential magnitude is base on the mean magnitude of comparison stars whose error is smaller. • How to know the magnitude of comparison star? • If it is the standard star. The apparent magnitude has been cataloged. • However, in the most of cases, there is no standard star in the field. The magnitude of the comparison star must be calibrated. • A filed with standard star must be shot (at least once). • However, the angular separation between the comparison star and the standard star could be large so the effect of air mass must be also considered

  30. Differential Photometry • In studying the variation of the target, sometimes important value is the change of the apparent magnitude, not the apparent magnitude. • Thus the calibration of the comparison star is unnecessary,

  31. Light Curve from Differential Photometry Not Apparent but magnitude difference between target and comparison star

  32. Light Curve after Calibration Smaller magnitude (larger flux) above Larger magnitude (smaller flux) below

  33. Light Curve

  34. Air Mass • However, for the ground-based telescope, the observed star flux is affected by the atmosphere absorption/scattering F(0,0)>F(z,0)>F(z,θ) F(0,0) θ Atmosphere z F(z,0) F(z,θ)

  35. Absorption & Scattering • 大氣對可見光雖是透明，但仍會對可見光產生部分的吸收與散射，因此可見光觀測不得不考慮大氣吸收影響。 • 這就是為什麼天文台都要建在高山處，除了遠離光害，還有就是降低大氣吸收與擾動的影響。 • 事實上，大氣只為我們開了二扇窗口，一為可見光(含部分近紅外與近紫外)，另一個為無線電波波段。 • 水蒸氣對紅外產生強烈吸收。 • 氮、氧等X光γ-ray等產生強烈吸收

  36. Absorption & Scattering 吸收或散射物質 • For a specified wavelength λ • Infinitesimal thickness: ds Nλ Nλ+ dNλ 面積A ds

  37. Absorption & Scattering

  38. Absorption & Scattering

  39. Absorption & Scattering Iλ(0) Iλ(s) • Finite thickness s’ s

  40. Air Mass • However, for the ground-based telescope, the observed star flux is affected by the atmosphere absorption/scattering F(0,0)>F(z,0)>F(z,θ) F(0,0) θ Atmosphere z F(z,0) F(z,θ)

  41. Air Mass

  42. Air Mass mλ mλ(0,0) mλ(z,0) 2.4 2.6 2.8 3.0 secθ 2.0 1.0

  43. Air Mass and Differential Photometry Δθ Comparison star Target

  44. Extinction Effect • The small angle condition holds for most of the case. • However, colors of the stars would still cause systematic error …… • In general, the absorption coefficient is larger for the shorter wavelength in optical band, that is

  45. Scattering in Optical band …… • Large particle, size >> λ, for example cloud

  46. Scattering in Optical band …… • Medium particle, size ~ λ, for example dust in interstellar media

  47. Scattering in Optical band …… • Small particle, size << λ, for example molecules in air

  48. Why Sky Looks Blue during Day time

  49. Twilight

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