Hubble's Law and Cosmological Redshift

哈勃定律与宇宙学红移


Hubble's Law

哈勃定律             

In the 1920s, the American astronomer EdwinHubble and other astronomers attempted to measure distances to other galaxiesand to calculate the redshifts in the spectra of those galaxies. They graduallyamassed large amounts of data giving the (approximate) distances d to more than20 galaxies as well as the shift of the radiation wavelength, z, from eachgalaxy. Except for a few of the nearest galaxies, all of the galaxies appearedto be moving away from Earth, so their shift in wavelength is towards red.Because of this, z is also called cosmological redshift.

在上世纪20年代,美国天文学家埃德温哈勃和其他天文学家试图测量距离,计算到其他星系的星系的光谱红移。他们逐渐积累了大量的数据,给出了大约20个星系的距离,以及每个星系的辐射波长Z的移动。除了一些最近的星系外,所有星系似乎都在远离地球,所以它们的波长移向红色。正因为如此,Z也被称为宇宙学红移。             

Astronomers interpreted these redshifts ascaused by the motion of the galaxies away from us -- that is, as a kind ofDoppler shift (recall the discussion of Doppler shift in a previous lecture).The apparent recessional velocity v of a given galaxy could then be calculatedfrom the product of the redshift of its spectrum z and the speed of light c:

天文学家解释这些红移是由星系远离我们的运动引起的也就是说,这是一种多普勒频移(回想一下前一讲中关于多普勒频移的讨论)。一个给定星系的明显后退速度v可以从其光谱z的红移和光速c的速度计算出来:

v=zc

In 1929, Hubble plotted the distance andapparent recessional velocity of 24 galaxies in a single graph. The figurebelow shows Hubble's original plot, with recessional velocity on the verticalaxis

1929年,哈勃绘制了一个图中24个星系的距离和明显的后退速度。下图显示了哈勃的原图,在垂直轴上的后退速度和水平轴上的距离。          


From this linear plot, Hubble stated anempirical law relating a galaxy's distance from earth d to the apparent speedat which the galaxy is receding from the earth v:

 从这一线性图中,哈勃描述了一个有关星系距离地球d的经验定律,与银河系从地球v后退的表观速度有关:

v=Hd

where H is the slope of the best-fit lineto the data. H is known as the Hubble constant.

其中H是数据的最适合行的斜率。H被称为哈勃常数。             

Using the fact that a galaxy's recessionalvelocity is v=zc, Hubble's lawcan be also expressed in the form:

使用一个星系的后退的速度v = zc,哈勃定律也可以表达成这个形式:

zc=Hd

Hubble's graph and empirical law changedthe way the redshifts of distant galaxies were interpreted. Rather thaninterpreting observed redshift in the spectrum of a galaxy as due to the(apparent) velocity of the galaxy moving away from us through space, Hubble'slaw led astronomers and physicists to interpret that redshift as a"cosmological redshift" due to the expansion of inter-galactic space.

 哈勃图和实证法改变了遥远星系的红移的解释。哈勃定律并没有解释银河系中观测到的红移现象,而是由于星系在空间上远离我们而产生的明显的速度,哈勃定律将天文学家和物理学家们解释为由于星系间空间的扩展,红移是一种“宇宙学红移”。             

So how do astronomers obtain a measure ofthe redshift of a star or a galaxy? And what exactly do they mean ininterpreting that redshift as "cosmological"?

那么天文学家如何获得恒星或星系红移的测量呢?在解释红移为“宇宙学”时,它们的确切含义是什么?

Cosmological Redshift

宇宙学红移             

Astronomers can calculate cosmologicalredshift based on direct observations (independently of knowing the actualdistances between different celestial bodies) by means of a spectrograph. Aspectrograph is an instrument that separates incoming light (such as from astar or galaxy) into its different frequencies (wavelengths). Recall that aprism always separates light into a continuous rainbow spectrum (red, orange,yellow, green, blue, indigo, violet). Higher frequencies correspond to shorterwavelengths, which are "bluer" light (i.e., the violet end of thespectrum). Lower frequencies correspond to longer wavelengths, which are"redder" light (i.e., the red end of the spectrum).

天文学家可以通过直接观测来计算宇宙学红移(不依赖于知道不同天体之间的实际距离)。摄谱仪是把入射光(如恒星或星系)分成不同频率(波长)的仪器。回想一下,棱镜总是把光线分为连续的彩虹光谱(红、橙、黄、绿、蓝、靛、紫)。更高的频率对应较短的波长,即“更蓝”的光(即光谱的紫端)。较低的频率对应的波长较长,这是“红”光(即红端的频谱)。

  

However, since stars and galaxies are notpure electromagnetic radiation -- rather, they contain elements such ashydrogen, helium, oxygen, sodium, calcium, etc. -- their spectrum is not acontinuous rainbow of colors, but rather is broken by dark lines. The positionsof the lines occur at particular wavelengths (or, equivalently, at particularfrequencies) that are characteristic for a given element. A dark line occurs ata particular wavelength (frequency) because the photons of that wavelength(frequency) are unable to be emitted by the star (rather, photons of thatenergy are being absorbed as electrons in the elements change in energy state).

然而,由于恒星和星系并不是纯粹的电磁辐射,相反,它们含有氢、氦、氧、钠、钙等元素,它们的光谱不是连续的彩色彩虹,而是被暗线破坏。线的位置发生在特定的波长(或等效地,在特定的频率)上,这是给定元素的特征。暗线在特定波长(频率)发生,因为波长(频率)的光子无法由恒星发出(相反,光子的能量被吸收,因为电子在能量状态中发生变化)。

       

By using the spectrograph to analyze thespectral lines produced by neutral hydrogen gas in a laboratory here on Earth,scientists know the characteristic spectral pattern for neutral hydrogen (thatis, at what wavelengths dark spectral lines will occur). Let us say thespectral lines appear at wavelengths of 410 nm, 434 nm, 486 nm, and 656 nm.(The unit "nm" stands for "nano-meter," which is 10−9 meters.) If we then analyze the spectral lines from a distantgalaxy, we might be surprised that the characteristic pattern of lines forneutral hydrogen do occur, but that they do not occur at the same wavelengthsas in the laboratory. They all are shifted such that the wavelengths arelonger, say at 414 nm, 438 nm, 491 nm, and 663 nm. This shift toward the longerwavelength, "redder," part of the spectrum is what we mean by"redshift." The redshift quantifies how much "redder" theobserved spectrum from a distant celestial body has become.

利用摄谱仪分析地球上一个实验室中性氢气体产生的光谱线,科学家知道中性氢的特征光谱模式(也就是说,在什么波长的暗谱线会出现)。让我们说光谱线出现在波长410纳米,434纳米,486纳米和656纳米。(单位“纳米”代表“纳米”这10−9米。)如果我们再分析谱线从一个遥远的星系,我们可能会感到惊讶,为中性氢线的特征模式确实发生,但它们不发生在同一个波长在实验室。它们都被移动,使得波长更长,比如说在414纳米、438纳米、491纳米和663纳米。这种转向更长的波长,”红,“频谱的部分就是我们所说的“红移”。红移量化多少“红”所观察到的光谱已经成为遥远的天体。

Why does this redshift occur for lightemitted by a distant galaxy? In the new interpretation based on Hubble's law,this "cosmological redshift" is caused by the expansion of space --by an increasing separation over time between Earth and the distant galaxy.That is, space was not static but was expanding, so that the redshifts werecaused by the expansion of space, not the proper velocities of the galaxies.(In fact, galaxies do have proper motions that impact the redshift, but forsimplicity here we are assuming the redshift is entirely due to thecosmological redshift caused by cosmic expansion.)

为什么这个红移发生在遥远星系发出的光?在基于哈勃定律的新解释中,这种“宇宙学红移”是由空间膨胀引起的,即随着地球与遥远星系之间时间的不断增加而分离。就是说,空间是不是静态的而是在扩大,所以,红移空间膨胀所导致的,不适当的星系的速度。(事实上,星系确实有影响红移的适当运动,但简单起见,我们假设红移完全是由宇宙膨胀引起的宇宙红移)。

When light is emitted from the distantgalaxy, it has exactly the same characteristic wavelengths as such lightemitted in our laboratory on Earth. But, over the period of millions orbillions of years during which the emitted light was traveling through space,space itself was expanding, causing the wavelengths of the emitted light to begradually "stretched" more and more, so that by the time the light isobserved here on Earth, the wavelengths are measured to be longer ("redder")than those in the laboratory on Earth. Thus, cosmological redshift quantifieshow much the wavelength of an observed spectral line has been"stretched" by cosmic expansion from its emitted wavelength to theobserved wavelength.

 当光线从遥远的星系发出时,它与我们实验室在地球上发出的光具有完全相同的特征波长。但是,在数百万或数十亿年,在这期间发出的光穿过空间内,空间本身的膨胀,导致发射的光的波长被逐渐“捉襟见肘”越来越多,这样的时候,光是在地球的观察,计算波长越长(“红”)在地球比在实验室的。因此,宇宙学红移量化了观测到的光谱线的波长被宇宙膨胀从其发射波长扩展到所观察到的波长。

The cosmological redshift z is defined tobe the fractional increase in wavelength of radiation emitted from a distantcelestial object due to the expansion of space:

宇宙红移z定义为宇宙空间膨胀引起的遥远天体辐射波长的分数增加:


The observed wavelength, λobserved,is the value of the wavelength of a spectral line for a distant celestial bodyas observed by us on Earth. The initial wavelength, λinitial, is thevalue of the wavelength of the corresponding spectral line in the radiationemitted by the celestial body (at the celestial body at the time of emission).

观察到的波长,λ观察,是一个谱线的波长值为一个遥远的天体,我们观察到在地球。初始波长,λ初始,是对应的谱线的天体发出的辐射的波长值(在天体在发射时间)。


Photo of Einstein and Hubble, taken duringone of Einstein's visits to the Mount Wilson Observatory in the mountains nearPasadena, California.

爱因斯坦和哈勃的照片,摄于爱因斯坦在帕萨迪纳加利福尼亚附近山上威尔逊山天文台的一次访问中。