哈勃定律
维库，知识与思想的自由文库
| 物理宇宙學 |
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| 物理宇宙學 |
| 早期的宇宙 |
| 膨脹的宇宙 |
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紅移 • 哈勃定律 |
| 結構形成 |
| 成分 |
| 歷史 |
| 宇宙論實驗 |
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觀測的宇宙論 |
| 科學家 |
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愛因斯坦 • 弗里德曼 • 勒梅特 |
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哈勃定律是物理宇宙論的陳述：來自遙遠星系光線的紅移與他們的距離成正比。這條定律是哈勃和米爾頓·修默生在接近十年的觀測之後，於1929年首先公式化的。 [1]它被認為是在擴展空間範例上的第一個觀察依據，和今天經常被援引作為支持大爆炸的一個重要證據。這個常數的最佳數值是在2003年使用人造衛星威爾金森微波各向異性探測器(WMAP)測得的，數值為71 ± 4 (公里/秒)/Mpc。在2006年的資料，圖中對應的是70+2.4−3.2
(km/s)/Mpc。
在宇宙学研究中，哈勃定律成为宇宙膨胀理论的基础。但哈勃定律中的速度和距离均是间接观测得到的量。速度——距离关系和速度——视星等关系，是建立在观测红移——视星等关系及一些理论假设前提上的。哈勃定律原来由对正常星系观测而得，现已应用到类星体或其他特殊星系上。哈勃定律通常被用来推算遥远星系的距离。
哈勃定律 ( Hubble's law )
Vf = Hc x D
參數說明：
Vf：Velocity ( Far Away ) 遠離速率 單位：km / s
Hc：Hubble's Constant 哈勃常數 單位：km / (s．Mpc)
D：Distance 相對地球的距離 單位：Mpc 百萬秒差距
目录 |
[编辑] 發現
In the decade before Hubble made his observations, a number of physicists and mathematicians had established a consistent theory of the relationship between space and time by using Einstein's field equation of general relativity. Applying the most general principles to the question of the nature of the universe yielded a dynamic solution that conflicted with the then prevailing notion of a static Universe.
However, a few scientists continued to pursue the dynamical universe and discovered that it could be characterized by a metric that came to be known after its discoverers, namely Friedmann, Lemaître, Robertson, and Walker. When this metric was applied to the Einstein equations, the so-called Friedmann equations emerged which characterized the expansion of the universe based on a parameter known today as the scale factor which can be considered a scale invariant form of the proportionality constant of Hubble's Law. This idea of an expanding spacetime would eventually lead to the Big Bang and to the Steady State theories.
Edwin Hubble did most of his professional astronomical observing work at Mount Wilson observatory, at the time the world's most powerful telescope. His observations of Cepheid variable stars in spiral nebulae enabled him to calculate the distances to these objects. Surprisingly these objects were discovered to be at distances which placed them well outside the Milky Way. The nebulae were first described as "island universes" and it was only later that the moniker "galaxy" would be applied to them.
Combining his measurements of galaxy distances with Vesto Slipher's measurements of the redshifts associated with the galaxies, Hubble discovered a rough proportionality of the objects' distances with their redshifts. Though there was considerable scatter (now known to be due to peculiar velocities), Hubble was able to plot a trend line from the 46 galaxies he studied and obtained a value for the Hubble constant of 500 km/s/Mpc, which is much higher than the currently accepted value due to errors in his distance calibrations. Such errors in determining distance continue to plague modern astronomers. (See the article on cosmic distance ladder for more details.)
In 1958 the first good estimate of H0, 75 km/s/Mpc, was published (by Allan Sandage). But it would be decades before a consensus was achieved (see 'Measuring the Hubble constant' below).
After Hubble's discovery was published, Albert Einstein abandoned his work on the cosmological constant which he had designed to allow for a static solution to his equations. He would later term this work his "greatest blunder" since the belief in a static universe was what prevented him from predicting the expanding universe. Einstein would make a famous trip to Mount Wilson in 1931 to thank Hubble for providing the observational basis for modern cosmology.
[编辑] 說明
The discovery of the linear relationship between recessional velocity and distance yields a straightforward mathematical expression for Hubble's Law as follows:
- v = H0D
where v is the recessional velocity due to redshift, typically expressed in km/s. H0 is Hubble's constant and corresponds to the value of H (often termed the Hubble parameter which is a value that is time dependent) in the Friedmann equations taken at the time of observation denoted by the subscript 0. This value is the same throughout the universe for a given conformal time. D is the proper distance that the light had traveled from the galaxy in the rest frame of the observer, measured in megaparsecs: Mpc.
For relatively nearby galaxies, the velocity v can be estimated from the galaxy's redshift z using the formula v = zc where c is the speed of light. For far away galaxies, v can be determined from the redshift z by using the relativistic Doppler effect. However, the best way to calculate the recessional velocity and its associated expansion rate of spacetime is by considering the conformal time associated with the photon traveling from the distant galaxy. In very distant objects, v can be larger than c. This is not a violation of the special relativity however because a metric expansion is not associated with any physical object's velocity.
In using Hubble's law to determine distances, only the velocity due to the expansion of the universe can be used. Since gravitationally interacting galaxies move relative to each other independent of the expansion of the universe, these relative velocities, called peculiar velocities, need to be accounted when applying Hubble's law. The Finger of God effect is one result of this phenomenon discovered in 1938 by Benjamin Kenneally. Systems that are gravitationally bound, such as galaxies or our planetary system, are not subject to Hubble's law and do not expand.
The mathematical derivation of an idealized Hubble's Law for a uniformly expanding universe is a fairly elementary theorem of geometry in 3-dimensional Cartesian/Newtonian coordinate space, which, considered as a metric space, is entirely homogeneous and isotropic (properties do not vary with location or direction). Simply stated the theorem is this:
- Any two points which are moving away from the origin, each along straight lines and with speed proportional to distance from the origin, will be moving away from each other with a speed proportional to their distance apart.
The value of Hubble parameter changes over time either increasing or decreasing depending on the sign of the so-called deceleration parameter q which is defined by:
In a universe with a deceleration parameter equal to zero, it follows that H = 1/t, where t is the time since the Big Bang. A non-zero, time-dependent value of q simply requires integration of the Friedmann equations backwards from the present time to the time when the comoving horizon size was zero.
We may define the "Hubble age" (also known as the "Hubble time" or "Hubble period") of the universe as 1/H, or 977793 million years/[H/(km/s/Mpc)]. The Hubble age comes to 13968 million years for H=70 km/s/Mpc, or 13772 million years for H=71 km/s/Mpc. The distance to a galaxy being approximately zc/H for small redshifts z, and expressing c as 1 light-year per year, this distance can be expressed simply as z times 13772 million light-years.
It was long thought that q was positive, indicating that the expansion is slowing down due to gravitational attraction. This would imply an age of the universe less than 1/H (which is about 14,000 million years). For instance, a value for q of 1/2 (one theoretical possibility) would give the age of the universe as 2/(3H). The discovery in 1998 that q is apparently negative means that the universe could actually be older than 1/H. In fact, independent estimates of the age of the universe come out fairly close to 1/H
[编辑] 奧伯斯佯謬
哈勃定律對大爆炸的解釋總結了空間的擴展與著名的古老難題奧伯斯佯謬之間的矛盾：如果宇宙是無限的、穩定的，充滿了均勻分布的恆星，那麼在天空中視線所及之處都將存在著恆星，而天空也將會像恆星的表面一樣明亮。從1600年代開始，天文學家和其他的思想家提出了許多可能解決這個佯繆的想法，但當前能被接受的這一部分是來自大爆炸的理論。宇宙只存在了有限的時間，只有有限多的星光有機會到達我們這兒，所以矛盾就解決了。換言之，在膨脹的宇宙中，遠方天體的退行速度使來自她們的星光產生紅移並且降低了亮度，但這樣也只是解決了部份的矛盾。依照大爆炸的理論，兩者都有貢獻(宇宙的歷史是有限的在兩者中較為重要)。 天空之所以黑暗，也為大爆炸提供了一種證據。[2]
[编辑] 哈勃常數的測量
在二十世紀後半，哈勃常數H0的值被估計約在50至90(km/s)/Mpc之間。
哈勃常數的值曾是個長久而激烈的爭議主題，Gérard de Vaucouleurs主張其值應為80而Allan Sandage則認為其應為40。1996年，由John Bahcall主持，包含Gustav Tammann及Sidney van den Bergh的辯論以類似早期Shapley-Curtis debate的模式舉行，主題針對上述兩個競爭數值。1990年代晚期，引進宇宙的λ-CDM模型，數值差異的問題被部分地解決。在此模型下，利用苏尼亚耶夫-泽尔多维奇效应進行的X光高紅移群及微波波長的觀察、宇宙微波背景辐射各向异性的量度和光學調查皆測定哈勃常數的值為70左右。特別的是，Hubble Key Project（由Wendy L. Freedman博士主導，在卡內基天文台進行）進行最精確的光學測量，在2001年五月發表其最終估計值為72±8 (km/s)/Mpc，此結果與基於苏尼亚耶夫-泽尔多维奇效应進行的銀河系星群觀測所測出的H0相當一致，具有相似的精確值。在2003年，利用WMAP所得出最高精度的宇宙微波背景辐射測定值為71±4 (km/s)/Mpc，而直到2006年，皆以70 (km/s)/Mpc, +2.4/-3.2作為測定值。因為1秒差距接近
公尺，故在公制單位中H0的值約為
(m/s)/m（Hertz）。從上述三種方法得出一致的測定值提供了H0測定值與λ-CDM模型有力的支持。
q的值被以Ia型超新星所制定的標準燭光觀察標準所測量。該標準定於1998年，其值被定為負值。此舉使許多天文學家感到驚訝，因為這暗示著宇宙膨脹正在「加速」（雖然哈勃因子隨時間而遞減；詳見暗物質及λ-CDM模型）。
在2006年八月，利用美國太空總署（NASA）的Chandra X光天文台（Chandra X-ray Observatory），來自NASA Marshall Space Flight Center（MSFC）的研究小組觀測得出哈勃常數的值為77公里每秒每百萬秒差距（77km/s Mpc；1百萬秒差距等於3.26百萬光年），不準量約15%。 [3]
[编辑] 注解
- ↑ 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)
- ↑ S. I. Chase, Olbers' Paradox, entry in the Physics FAQ; see also I. Asimov, "The Black of Night", in Asimov on Astronomy (Doubleday, 1974), ISBN 0-385-04111-X.
- ↑ Chandra independently determines Hubble constant in Spaceflight Now Chandra獨立測出哈勃常數的新聞刊登在「Spaceflight Now」網站
[编辑] 相關條目
[编辑] 參考資料
- Kutner, Marc (2003). Astronomy: A Physical Perspective. Cambridge University Press. ISBN 0-521-52927-1.
- Hubble, E.P.., The Observational Approach to Cosmology (Oxford, 1937)
[编辑] 外部鏈結
- History of Hubble's constant by John Huchra
- The Hubble Key Project
- Final Results from the Hubble Space Telescope Key Project to Measure the Hubble Constant. Freedman et. al. The Astrophysical Journal, Volume 553, Issue 1, pp. 47-72.
- The Hubble Diagram Project
