# 紅移

$Z = \frac{\lambda - \lambda_0}{\lambda_0} = \frac{f_0 - f}{f}$

## 分類

• 多普勒紅移：物体和观察者之间的相对运动可以导致红移，与此相对应的红移称为多普勒红移，是由多普勒效应引起的。
• 重力紅移：根据广义相对论重力場中发射出来时也会发生红移的现象。这种红移称为重力紅移
• 宇宙學紅移：20世纪初，美国天文学家埃德温·哈勃发现，观测到的绝大多数星系的光谱线存在红移现象。这是由於宇宙空间在膨胀，使天体發出的光波被拉長，谱线因此“变红”，这稱為宇宙學紅移，并由此得到哈勃定律。20世纪60年代发现了一类具有极高红移值的天体：类星体，成为近代天文学中非常活跃的研究领域。

## 測量、特性和解釋

$z = \frac{\lambda_{\mathrm{observed}} - \lambda_{\mathrm{emitted}}}{\lambda_{\mathrm{emitted}}}$ $z = \frac{f_{\mathrm{emitted}} - f_{\mathrm{observed}}}{f_{\mathrm{observed}}}$
$1+z = \frac{\lambda_{\mathrm{observed}}}{\lambda_{\mathrm{emitted}}}$ $1+z = \frac{f_{\mathrm{emitted}}}{f_{\mathrm{observed}}}$

z被測量後，紅移和藍移的差別只是簡單的正負號的區別。依據下一章節的機制，無論被觀察到的是紅移或藍移，都有一些基本的說明。例如，都卜勒效應的藍移（z < 0）會聯想到物體朝向觀測者接近並且能量增加，反過來說都卜勒紅移（z > 0），就會聯想到物體遠離觀測者而去並且能量減少。同樣的，愛因斯坦效應的藍移可以聯想到光線進入強引力場，而愛因斯坦效應的紅移是離開引力場。

## 機制

### 都卜勒效應

$z \approx \frac{v}{c}$     (Since $\gamma \approx 1$, 參考下面的說明)

### 相對論的都卜勒效應

$1 + z = \left(1 + \frac{v}{c}\right)\gamma$

$1+ z = \frac{1 + v \cos(\theta)/c}{\sqrt{1-v^2/c^2}}$

$1 + z = \sqrt{\frac{1 + \frac{v}{c}}{1 - \frac{v}{c}}}$

### 膨脹的宇宙

$1+z = \frac{a_{\mathrm{now}}}{a_{\mathrm{then}}}$

### 重力紅移

$1+z=\frac{1}{\sqrt{1-\left(\frac{2GM}{rc^2}\right)}}$,

• $G$重力常數
• $M$是產生引力場的質量
• $r$是觀測者的徑向坐標（這類似於傳統中由中心至觀測者的距離，但實際是史瓦西坐标），和
• $c$光速

## 天文學的觀測

### 外星系的觀察

1. 星系之間相互的重力吸引會減緩宇宙的擴張行動
2. 可能存在的宇宙常數第五元素與可能會改變宇宙擴張的速率。

[47] 最近的觀測卻建議宇宙的擴張不僅沒有如同第一點的預測減速，反而在加速中。[48][49]這是廣泛的，雖然不是相當普遍的，相信這是因為有暗物質在控制著宇宙的發展。這樣的宇宙常數暗示宇宙的最後命運不是大擠壓，反而可預見宇宙將長久存在。（可是在宇宙內多數的物理程序仍然朝向熱死亡。）

### 紅移巡天

2度視場星系紅移巡天資料最精華的資料

## 參考資料

1. ^ See Feynman, Leighton and Sands（1989）or any introductory undergraduate（and many high school）physics textbooks. See Taylor（1992）for a relativistic discussion.
2. ^ 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 See Binney and Merrifeld（1998）,Carroll and Ostlie（1996）,Kutner（2003）for applications in astronomy.
3. ^ 参见Misner, Thorne, Wheeler (1973)等人或Weinberg (1971)关于宇宙学的著作.
4. ^ 参见Misner, Thorne, Wheeler (1973)等人或Weinberg (1971)关于宇宙学的著作.
5. ^ Doppler, Christian, "Beitrage zur fixsternenkunde" (1846), Prag, Druck von G. Haase sohne
6. ^ Dev Maulik, "Doppler Sonography: A Brief History" in Doppler Ultrasound in Obstetrics And Gynecology（2005）by Dev（EDT）Maulik, Ivica Zalud
7. ^ O'Connor, John J.; Robertson, Edmund F., Doppler, MacTutor History of Mathematics archive
8. ^ 8.0 8.1 William Huggins, "Further Observations on the Spectra of Some of the Stars and Nebulae, with an Attempt to Determine Therefrom Whether These Bodies are Moving towards or from the Earth, Also Observations on the Spectra of the Sun and of Comet II." (1868) Philosophical Transactions of the Royal Society of London, Volume 158, pp. 529-564
9. ^ Reber, G., "Intergalactic Plasma"(1995) Astrophysics and Space Science, v. 227, p. 93-96.
10. ^ Bélopolsky, A., "On an Apparatus for the Laboratory Demonstration of the Doppler-Fizeau Principle" (1901) Astrophysical Journal, vol. 13, p.15
11. ^ Slipher first reports on his measurement in the inaugural volume of the Lowell Observatory Bulletin, pp.2.56-2.57[1]. His article entitled The radial velocity of the Andromeda Nebula reports making the first Doppler measurement on September 17, 1912. In his report Slipher writes: "The magnitude of this velocity, which is the greatest hitherto observed, raises the question whether the velocity-like displacement might not be due to some other cause, but I believe we have at present no other interpretation for it." Three years later, in the journal Popular Astronomy, Vol. 23, p. 21-24 [2], Slipher wrote a review entitled Spectrographic Observations of Nebulae. In it he states, "The early discovery that the great Andromeda spiral had the quite exceptional velocity of - 300 km（/s）showed the means then available, capable of investigating not only the spectra of the spirals but their velocities as well." Slipher reported the velocities for 15 spiral nebulae spread across the entire celestial sphere, all but three having observable "positive" (that is recessional) velocities.
12. ^ Hubble, Edwin, "A Relation between Distance and Radial Velocity among Extra-Galactic Nebulae" (1929) Proceedings of the National Academy of Sciences of the United States of America, Volume 15, Issue 3, pp. 168-173 (Full article, PDF)
13. ^ 13.0 13.1 This was recognized early on by physicists and astronomers working in cosmology in the 1930s. The earliest layman publication describing the details of this correspondence was Sir Arthur Eddington's book The Expanding Universe: Astronomy's 'Great Debate', 1900-1931, published by Press Syndicate of the University of Cambridge in 1933.
14. ^ See, for example, this 25 May 2004 press release from NASA's Swift space telescope that is researching gamma-ray bursts: "Measurements of the gamma-ray spectra obtained during the main outburst of the GRB have found little value as redshift indicators, due to the lack of well-defined features. However, optical observations of GRB afterglows have produced spectra with identifiable lines, leading to precise redshift measurements."
15. ^ Where z = 紅移; v = 速度; c = 光速; γ = 勞侖茲因子; a = 尺度因素; G = 萬有引力常數; M = 物體質量; r = radial Schwarzschild coordinate
16. ^ H. Ives and G. Stilwell, An Experimental study of the rate of a moving atomic clock , J. Opt. Soc. Am. 28, 215-226（1938）[3]
17. ^ See "Photons, Relativity, Doppler shift" at the University of Queensland
18. ^ The distinction is made clear in Harrison, E.R. 1981 Cosmology: The Science of the Universe (New York: Cambridge University Press).
19. ^ This is only true in a universe where there are no peculiar velocities. Otherwise, redshifts combine as
$1+z=(1+z_{\mathrm{Doppler}})(1+z_{\mathrm{expansion}})$
which yields solutions where certain objects that "recede" are blueshifted and other objects that "approach" are redshifted. For more on this bizarre result see Davis, T. M., Lineweaver, C. H., and Webb, J. K. "Solutions to the tethered galaxy problem in an expanding universe and the observation of receding blueshifted objects", American Journal of Physics（2003）,71 358-364.
20. ^ Peebles (1993).
21. ^ Measurements of the peculiar velocities out to 5 Mpc using the Hubble Space Telescope were reported in 2003 by Karachentsev et al. Local galaxy flows within 5 Mpc. 02/2003 Astronomy and Astrophysics, 398, 479-491.[4]
22. ^ University of Massachusetts, Amherst professor Edward Harrison gives a review summary of this confusion in his paper The redshift-distance and velocity-distance laws（01/1993 Astrophysical Journal, Part 1 (ISSN 0004-637X）,403, no. 1, p. 28-31.) [5]
23. ^ Odenwald & Fieberg 1993
24. ^ This is because the expansion of the spacetime metric is describable by general relativity and dynamically changing measurements as opposed to a rigid Minkowski metric. Space, not being composed of any material can grow faster than the speed of light since, not being an object, it is not bound by the speed of light upper bound.
25. ^ M. Weiss, What Causes the Hubble Redshift?, entry in the Physics FAQ（1994）,available via John Baez's website
26. ^ See for example, Chant, C. A., "Notes and Queries (Telescopes and Observatory Equipment-The Einstein Shift of Solar Lines)" (1930) Journal of the Royal Astronomical Society of Canada, Vol. 24, p.390
27. ^ Einstein, A. Unknown title. Jahrbuch der Radioaktivität und Elektronik. 1907, 4: 411–?.
28. ^ R. V. Pound and G. A. Rebka Jr., Apparent weight of photons, Phys. Rev. Lett. 4, 337 (1960). [6] This paper was the first measurement.
29. ^ Sachs, R. K.; Wolfe, A. M.. Perturbations of a cosmological model and angular variations of the cosmic microwave background. Astrophysical Journal. 1967, 147 (73).
30. ^ When cosmological redshifts were first discovered, Fritz Zwicky proposed an effect known as tired light. While usually considered for historical interests, it is sometimes, along with intrinsic redshift suggestions, utilized by nonstandard cosmologies. In 1981, H. J. Reboul summarised many alternative redshift mechanisms that had been discussed in the literature since the 1930s. In 2001, Geoffrey Burbidge remarked in a review that the wider astronomical community has marginalized such discussions since the 1960s. Burbidge and Halton Arp, while investigating the mystery of the nature of quasars, tried to develop alternative redshift mechanisms, and very few of their fellow scientists acknowledged let alone accepted their work.
31. ^ For a review of the subject of photometry, consider Budding, E., Introduction to Astronomical Photometry, Cambridge University Press（September 24, 1993）,ISBN 0-521-41867-4
32. ^ The technique was first described by Baum, W. A.: 1962, in G. C. McVittie（ed.）,Problems of extra-galactic research, p. 390, IAU Symposium No. 15
33. ^ Bolzonella, M.; Miralles, J.-M.; Pelló, R., Photometric redshifts based on standard SED fitting procedures, Astronomy and Astrophysics, 363, p.476-492 (2000).
34. ^ A pedagogical overview of the K-correction by David Hogg and other members of the SDSS collaboration can be found at astro-ph.
35. ^ The Exoplanet Tracker is the newest observing project to use this technique, able to track the redshift variations in multiple objects at once, as reported in Ge, Jian et al. The First Extrasolar Planet Discovered with a New-Generation High-Throughput Doppler Instrument, The Astrophysical Journal, 2006 648, Issue 1, pp. 683-695.[7]
36. ^ Libbrecht, Ken G., Solar and stellar seismology, Space Science Reviews, 1988 37 n. 3-4, 275-301.
37. ^ In 1871 Hermann Carl Vogel measured the rotation rate of Venus. Vesto Slipher was working on such measurements when he turned his attention to spiral nebulae.
38. ^ An early review by Oort, J. H. on the subject: The formation of galaxies and the origin of the high-velocity hydrogenAstronomy and Astrophysics, 7, 381（1970）[8].
39. ^ Asaoka, Ikuko, X-ray spectra at infinity from a relativistic accretion disk around a Kerr black hole, Astronomical Society of Japan, Publications（ISSN 0004-6264）,41 no. 4, 1989, p. 763-778 [9]
40. ^ Rybicki, G. B. and A. R. Lightman, Radiative Processes in Astrophysics, John Wiley & Sons, 1979, p. 288 ISBN 0-471-82759-2
41. ^ An accurate measurement of the cosmic microwave background was achieved by the COBE experiment. The final published temperature of 2.73 K was reported in this paper: Fixsen, D. J.; Cheng, E. S.; Cottingham, D. A.; Eplee, R. E., Jr.; Isaacman, R. B.; Mather, J. C.; Meyer, S. S.; Noerdlinger, P. D.; Shafer, R. A.; Weiss, R.; Wright, E. L.; Bennett, C. L.; Boggess, N. W.; Kelsall, T.; Moseley, S. H.; Silverberg, R. F.; Smoot, G. F.; Wilkinson, D. T.. (1994). "Cosmic microwave background dipole spectrum measured by the COBE FIRAS instrument", Astrophysical Journal, 420, 445. The most accurate measurement as of 2006 was achieved by the WMAP experiment.
42. ^ Fan, Xiahoui et al., A Survey of z>5.7 Quasars in the Sloan Digital Sky Survey. II. Discovery of Three Additional Quasars at z>6, The Astronomical Journal（2003）,v. 125, Issue 4, pp. 1649-1659 [10].
43. ^ Egami, E., et al., Spitzer and Hubble Space Telescope Constraints on the Physical Properties of the z~7 Galaxy Strongly Lensed by A2218, The Astrophysical Journal（2005）,v. 618, Issue 1, pp. L5-L8 [11].
44. ^ Pelló, R., Schaerer, D., Richard, J., Le Borgne, J.-F., & Kneib, J.P., ISAAC/VLT observations of a lensed galaxy at z = 10.0, Astronomy and Astrophysics（2004）,416, L35 [12].
45. ^ Peebles (1993).
46. ^ Binney, James; and Scott Treimane. Galactic dynamics. Princeton University Press. ISBN 0-691-08445-9.
47. ^ P. J. E. Peebles and Bharat Ratra. The cosmological constant and dark energy. Reviews of Modern Physics. 2003, 75: 559–606.
48. ^ S. Permutter et al. (The Supernova Cosmology Project). Measurements of Omega and Lambda from 42 high redshift supernovae. Astrophysical J. 1999, 517: 565–86.
49. ^ Adam G. Riess et al. (Supernova Search Team). Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astronomical J. 1998, 116: 1009–38.
50. ^ Peebles (1993:8, 77).
51. ^ Weinberg（1971, pp. 595–6）,Misner, Thorne and Wheeler (1973, §28.3).
52. ^ M. J. Geller & J. P. Huchra, Science 246, 897 (1989). online
53. ^ See the official CfA website for more details.
54. ^ Shaun Cole et al. (The 2dFGRS Collaboration). The 2dF galaxy redshift survey: Power-spectrum analysis of the final dataset and cosmological implications. Mon. Not. Roy. Astron. Soc. 2005, 362: 505–34. 2dF Galaxy Redshift Survey homepage
55. ^ SDSS Homepage
56. ^ Marc Davis et al. (DEEP2 collaboration). Science objectives and early results of the DEEP2 redshift survey. Conference on Astronomical Telescopes and Instrumentation, Waikoloa, Hawaii, 22-28 Aug 2002. 2002.

### 論文

• Odenwald, S. & Fienberg, RT. 1993; "Galaxy Redshifts Reconsidered" in Sky & Telescope Feb. 2003; pp31-35（This article is useful further reading in distinguishing between the 3 types of redshift and their causes.）
• Lineweaver, Charles H. and Tamara M. Davis, "Misconceptions about the Big Bang", Scientific American, March 2005. (This article is useful for explaining the cosmological redshift mechanism as well as clearing up misconceptions regarding the physics of the expansion of space.)