Luminosity & the Cosmos
A-Level Physics Topic 25 12:42 English narration · English + 中文 subtitles burned in
Chapters
Transcript
That star is a hundred trillion kilometres away.
那颗星在一百万亿公里之外。
You will never touch it.
你永远碰不到它。
You will never visit it.
你永远到不了它。
And yet, from its faint light alone — just the light that falls on your eye — we can measure its true power, its temperature, its size, even how fast the whole Universe is flying apart.
然而，仅仅凭着它微弱的光—— 仅仅是落在你眼睛里的那点光——我们就能量出它真正的功率、它的温度、它的大小， 甚至整个宇宙正以多快的速度飞散开来。
Everything we know about the cosmos, we read from light.
关于宇宙我们所知道的一切，都是从光里读出来的。
The whole Universe, decoded from starlight.
整个宇宙，从星光中被解读出来。
Today: luminosity and flux, standard candles, the temperature and size of stars, and the redshift that reveals an expanding Universe.
今天：光度与通量、标准烛光、恒星的温度和大小， 以及揭示宇宙膨胀的红移。
Let's begin.
让我们开始吧。
A star's luminosity is its total power — all the energy it pours out every second, in every direction.
一颗恒星的光度，就是它的总功率——它每秒钟朝四面八方倾泻出的全部能量。
But by the time that light reaches us, it has spread out over an enormous sphere.
但等到那光到达我们时，它已经在一个巨大的球面上散开了。
So what we actually measure is the flux: the power falling on each square metre.
所以我们真正测到的是通量： 落在每一平方米上的功率。
Since the sphere's area grows as the distance squared, the flux drops as the distance squared.
由于球面的面积随距离的平方增大，通量就随距离的平方减小。
Double the distance, and the flux falls to a quarter.
距离加倍，通量降到四分之一。
This is the inverse-square law.
这就是平方反比定律。
Here is why the flux falls the way it does.
通量为什么会这样下降，原因就在这里。
The star emits a fixed power L in all directions.
恒星向各个方向发出固定的功率 L。
At distance d that power has spread over a sphere of area four pi d squared.
在距离 d 处，这份功率已经摊在一个面积为四 pi d 平方的球面上。
Go to twice the distance and the same light covers four times the area, so the flux is a quarter.
跑到两倍远处，同样多的光要覆盖四倍的面积，所以通量只剩四分之一。
Three times the distance, nine times the area, a ninth of the flux.
三倍远处，九倍的面积，九分之一的通量。
That is the inverse-square law, and the picture shows it directly: the patch grows as the square of the distance, so the power per unit area falls as the square of the distance.
这就是平方反比定律， 而这张图直接把它画了出来：小块的面积随距离的平方增大， 所以单位面积上的功率就随距离的平方下降。
The Sun's luminosity is three point eight times ten to the twenty-six watts.
太阳的光度是三点八乘以十的二十六次方瓦。
Find the radiant flux intensity at the Earth, one point five times ten to the eleventh metres away.
求距离一点五乘以十的十一次方米处、 也就是地球上的辐射通量密度。
Use F equals L over four pi d squared.
用 F 等于 L 除以四 pi d 平方。
Watch the squaring of a power of ten — that is where the arithmetic goes wrong.
注意十的幂次要平方——算术出错往往就在这一步。
The answer is about one point four times ten cubed watts per square metre, which is the solar constant, and worth recognising.
答案约为一点四乘以十的三次方 瓦每平方米，这就是太阳常数，值得记住。
Now run it the other way, because that is the useful direction: a telescope measures F, so if you know L, then d equals the square root of L over four pi F.
现在把它反过来用，因为那才是有用的方向： 望远镜测出的是 F，所以如果你知道 L，那么 d 就等于 L 除以四 pi F 的平方根。
That single rearrangement is the whole basis of measuring cosmic distances.
仅仅是这一次移项，就构成了测量宇宙距离的全部基础。
A standard candle is an object whose luminosity is known from its TYPE — you do not have to measure it.
标准烛光是这样一种天体：它的光度可以由它的类型直接得知——你不必去测量它。
Two examples, and you should know why each works.
有两个例子，而你应当知道每一个为什么成立。
Cepheid variables are pulsating stars, and their pulsation period is tightly linked to their luminosity, as this graph shows: a longer period means a more luminous star.
造父变星是脉动的恒星， 它们的脉动周期与光度紧密相关，正如这张图所示：周期越长，恒星越亮。
So you time the pulsation and read off L.
所以你只要给脉动计时，就能读出 L。
Type Ia supernovae are white dwarfs that reach a critical mass and explode, and because that critical mass is always the same, the peak luminosity is always about the same.
Ia 型超新星是达到临界质量而爆发的白矮星， 而由于那个临界质量总是相同的，峰值光度也就总是差不多。
The crucial property in both cases: they give you L WITHOUT needing to know the distance first — which is exactly why they reach galaxies far beyond parallax.
两者共同的关键性质是：它们给出 L，而不需要先知道距离—— 这正是它们能够到达远超视差范围的星系的原因。
Now, here is the trick to measuring distance.
好，这里就是测量距离的诀窍。
If we somehow know a star's true luminosity, and we measure its flux, we can work backwards to its distance.
如果我们不知怎么地知道了一颗星真正的光度，又测出了它的通量， 我们就能倒推出它的距离。
An object whose luminosity we know is called a standard candle.
一个我们已知其光度的天体，就叫标准烛光。
Cepheid variable stars are perfect: they pulse, brighten and dim, and the time for one pulse tells us the luminosity.
造父变星最合适不过： 它们脉动，忽明忽暗，而一次脉动所用的时间就告诉我们它的光度。
Exploding supernovae of one type always peak at the same brightness.
某一类型的爆发超新星， 峰值亮度总是相同的。
These candles let us reach across the Universe.
这些烛光，让我们能够跨越整个宇宙。
The colour of a star reveals its heat.
一颗星的颜色，透露出它的温度。
Every hot object glows with a spread of colours, peaking at one wavelength.
每一个炽热的物体，都以一片连续的颜色发光， 并在某一个波长处达到峰值。
Wien's law says that peak wavelength, times the temperature, is a fixed constant.
维恩定律说，那个峰值波长乘以温度，是一个固定的常量。
So the hotter the star, the shorter the peak wavelength, and the bluer it looks.
所以恒星越热，峰值波长就越短，看上去就越蓝。
A cool star glows red; our Sun, yellow-white; the hottest stars, blue.
冷的星发红光；我们的太阳，黄白色； 最热的星，是蓝色的。
Just find the peak, and you have the temperature.
只要找到那个峰值，你就得到了温度。
A hot body gives out a continuous blackbody spectrum, and its peak sits at a wavelength set only by its temperature.
热的物体发出连续的黑体谱，而它的峰值所在的波长只由温度决定。
Wien's displacement law says lambda-max times T is a constant, about two point nine times ten to the minus three metre kelvin.
维恩位移定律说 lambda max 乘以 T 是一个常数，约为二点九乘以十的负三次方米开。
Look at the curves.
看这些曲线。
A hotter body radiates more at EVERY wavelength — the whole curve is higher — and its peak shifts to the left, towards the blue.
更热的物体在每一个波长上都辐射得更多——整条曲线都更高—— 而且它的峰值向左移动，朝着蓝端。
So a cool red star around three thousand kelvin peaks in the infrared; the Sun at fifty-eight hundred peaks near five hundred nanometres, in the visible; and a hot blue-white star at twenty thousand kelvin peaks in the ultraviolet.
所以约三千开的冷红星，峰值在红外； 五千八百开的太阳，峰值在五百纳米附近，落在可见光里； 而两万开的炽热蓝白星，峰值在紫外。
Measure lambda-max and you have the surface temperature.
测出 lambda max，你就得到了表面温度。
A star's blackbody spectrum peaks at five hundred nanometres.
某颗恒星的黑体谱在五百纳米处达到峰值。
Find its surface temperature, taking b as two point nine times ten to the minus three metre kelvin.
求它的表面温度， 取 b 为二点九乘以十的负三次方米开。
Rearrange Wien's law: T equals b over lambda max.
把维恩定律移项：T 等于 b 除以 lambda max。
Convert the nanometres first — five hundred nanometres is five times ten to the minus seven metres — and the answer is about five thousand eight hundred kelvin.
先把纳米换算掉——五百纳米就是五乘以十的负七次方米——答案约为五千八百开。
Sanity-check it: that is our own Sun, which is exactly why sunlight peaks in the middle of the visible range and why our eyes evolved to see there.
做个合理性检验：那正是我们自己的太阳， 这也正是阳光的峰值落在可见光中段、而我们的眼睛演化成看那个波段的原因。
Treat a star as a blackbody sphere and its luminosity is L equals four pi sigma r squared T to the fourth, with sigma the Stefan-Boltzmann constant.
把恒星当作一个黑体球，它的光度就是 L 等于四 pi sigma r 平方 T 的四次方， 其中 sigma 是斯特藩-玻尔兹曼常量。
Take a star of radius seven times ten to the eighth metres at five thousand eight hundred kelvin.
取一颗半径为七乘以十的八次方米、 表面温度为五千八百开的恒星。
Substituting gives about three point nine times ten to the twenty-six watts — the Sun again.
代入后得到约三点九乘以十的二十六次方瓦——又是太阳。
Now read the two dependences off the formula, because that is what gets examined.
现在从公式里读出那两个依赖关系，因为这正是要考的。
L goes as r squared: double the radius, four times the luminosity.
L 与 r 平方成正比：半径加倍，光度变成四倍。
And L goes as T to the FOURTH: double the temperature, sixteen times the luminosity.
而 L 与 T 的四次方成正比： 温度加倍，光度变成十六倍。
That fourth power is why a small change in surface temperature makes such an enormous difference to how bright a star is.
正是这个四次方， 使得表面温度的一点小变化，会让一颗恒星的亮度差出天壤之别。
Here is a routine that combines both laws, and it answers a real question: how do you find the radius of a star when you cannot see it as a disc at all?
下面这套流程把两条定律结合起来，而且它回答了一个真实的问题： 当你根本无法把一颗恒星看成一个圆面时，怎么求出它的半径？
Three steps.
分三步。
One: measure lambda max and get T from Wien's law.
第一：测出 lambda max，用维恩定律得到 T。
Two: find L from the flux and the distance, using L equals four pi d squared F.
第二：由通量和距离求出 L， 用 L 等于四 pi d 平方 F。
Three: solve the Stefan-Boltzmann law for r — r equals the square root of L over four pi sigma T to the fourth.
第三：把斯特藩-玻尔兹曼定律解出 r—— r 等于 L 除以四 pi sigma T 四次方之后再开平方根。
And that is genuinely how astronomers do it.
天文学家确实就是这样做的。
Every star except the Sun is a point of light in even the best telescope, yet we know their sizes, from nothing but their colour, their brightness and their distance.
除了太阳以外，每一颗恒星在再好的望远镜里也只是一个光点， 可我们仍然知道它们的大小，靠的不过是它们的颜色、亮度和距离。
Temperature and size together set the luminosity — through the Stefan-Boltzmann law.
温度和大小，一起决定了光度——这就靠斯特藩-玻尔兹曼定律。
A star's power is proportional to its surface area, and to its temperature raised to the fourth power.
一颗星的功率， 正比于它的表面积，也正比于它温度的四次方。
That fourth power is fierce: double the temperature, and the star shines sixteen times brighter.
那个四次方很凶猛：温度加倍， 这颗星就亮十六倍。
Combine this with Wien's law, and from a star's colour and its flux, we can even work out its radius — for a star we can never see as more than a dot.
把它和维恩定律结合起来，仅凭一颗星的颜色和它的通量， 我们甚至能算出它的半径——哪怕这颗星在我们眼里永远只是一个光点。
And light carries one last secret.
而光还带着最后一个秘密。
The spectral lines of distant galaxies are shifted towards the red — stretched to longer wavelengths.
遥远星系的谱线，都朝红端移动——被拉伸到更长的波长。
This redshift means the galaxies are rushing away from us.
这种红移意味着，星系正在离我们远去。
And the farther a galaxy, the faster it flees — that is Hubble's law, speed proportional to distance.
而星系越远，逃离得越快——这就是哈勃定律， 速度正比于距离。
Everything is flying apart, which means everything was once together.
一切都在飞散，这意味着一切曾经聚在一起。
Run the clock backwards, and you arrive at the Big Bang — some fourteen billion years ago.
把时钟倒着走， 你就来到了大爆炸——大约一百四十亿年前。
Here is what a redshift actually looks like.
红移实际看起来就是这个样子。
The same pattern of hydrogen absorption lines appears in both spectra — that is how you know it is hydrogen — but in the distant star the whole pattern has slid towards the red, the longer-wavelength end.
同样一套氢的吸收线在两条光谱里都出现—— 正是靠这一点你才知道它是氢——但在那颗遥远的恒星上，整套图样都朝红端、 也就是波长更长的一端滑了过去。
Read as a Doppler shift, it means the source is moving away.
按多普勒效应来读，它意味着光源正在远离。
For speeds well below light, delta lambda over lambda is approximately v over c, where delta lambda is the observed wavelength minus the emitted one.
对远低于光速的速度，delta lambda 比 lambda 约等于 v 比 c， 其中 delta lambda 是观测到的波长减去发出时的波长。
Take the handout's example: emitted at four point six two times ten to the minus seven metres, observed at four point nine one, so delta lambda is nought point two nine times ten to the minus seven, and v comes out at about one point nine times ten to the seventh metres per second.
拿讲义上的例子来说：发出时是四点六二乘以十的负七次方米， 观测到的是四点九一，所以 delta lambda 是零点二九乘以十的负七次方， 算出 v 约为一点九乘以十的七次方米每秒。
Almost every point of light in this image is a whole galaxy, and almost every one of them is redshifted.
这张图上几乎每一个光点都是一整个星系，而其中几乎每一个都发生了红移。
A few nearby ones are blueshifted by their own local motion, but the pattern is overwhelming.
少数几个近处的星系因为自身的局部运动而蓝移，但整体的图景压倒性地一致。
So galaxies are on average moving apart — and here is the part that matters, not just away from US, but from each other.
所以星系平均而言在彼此远离——而下面这一点才是关键： 不只是在远离我们，而是彼此在远离。
There is nothing special about our position.
我们所处的位置并没有什么特殊。
The picture to hold is not galaxies flying through space away from a centre, but the space between them stretching.
要在脑中建立的图像，不是星系在空间中从一个中心飞散出去， 而是它们之间的空间本身在被拉伸。
And more distant galaxies are redshifted more, which is the observation Hubble's law makes precise.
而且越远的星系红移越大， 这正是哈勃定律要精确表述的那个观测事实。
Plot recession speed against distance for many galaxies and the points lie on a straight line through the origin.
把许多星系的退行速度对距离画出来，这些点落在一条过原点的直线上。
That is Hubble's law: v is approximately H-nought times d, with H-nought the Hubble constant, about two point three times ten to the minus eighteen per second — and always work in SI units here.
这就是哈勃定律：v 约等于 H 零乘以 d，其中 H 零是哈勃常数， 约为二点三乘以十的负十八次方每秒——而且这里一定要用国际单位。
The galaxy from our earlier example, receding at one point nine times ten to the seventh metres per second, is therefore at d equals v over H-nought, about eight point three times ten to the twenty-four metres.
我们前面例子里那个以一点九乘以十的七次方米每秒退行的星系， 距离就是 d 等于 v 除以 H 零，约为八点三乘以十的二十四次方米。
Now run the whole thing backwards.
现在把整件事倒过来推。
If everything is separating at a speed proportional to its distance, then everything was together at a single time in the past — one over H-nought ago.
如果一切都在以正比于距离的速度分开， 那么在过去的某一个时刻，一切都聚在一起——就在一除以 H 零之前。
That gives an age of about four point three times ten to the seventeen seconds, roughly fourteen billion years.
由此得到的年龄约为四点三乘以十的十七次方秒，大致是一百四十亿年。
Running the expansion backwards gives a Universe that was once tiny, hugely dense and hot — the Big Bang.
把膨胀倒推回去，得到的是一个曾经极小、极致密、极热的宇宙——这就是大爆炸。
If a question asks for the evidence, there are four pieces and you should be able to name them.
如果题目问证据，一共有四条，你应当能把它们说出来。
The expansion itself.
膨胀本身。
The redshift of galaxies, increasing with distance, which is what shows the expansion is uniform.
星系的红移随距离增大，正是它表明这种膨胀是均匀的。
The cosmic microwave background — the leftover heat of that hot early state, now stretched all the way into microwaves.
宇宙微波背景——那个炽热早期状态留下的余热，如今已被拉伸到微波波段。
And the hydrogen and helium abundances, which match what nuclear physics predicts should have formed in the first few minutes.
以及氢和氦的丰度，它与核物理预言在最初几分钟里应当形成的比例相符。
Four independent lines pointing at the same conclusion.
四条互相独立的线索，指向同一个结论。
Finally, the picture that ties the whole topic together.
最后是把整章串起来的这张图。
No single method measures every distance, so astronomers use a ladder, and each rung is calibrated by the one below it.
没有哪一种方法能测量所有的距离， 所以天文学家使用一架阶梯，而每一级都由它下面的一级来标定。
Parallax works for nearby stars, using nothing but geometry.
视差适用于近处的恒星，靠的只是几何。
Those nearby stars include Cepheids, which calibrates the period-luminosity relation — so standard candles now work out to other galaxies.
这些近处的恒星里就有造父变星， 于是周期光度关系得到了标定——标准烛光从此可以用到别的星系上去。
Those galaxies give both a distance and a redshift, which calibrates Hubble's constant — so Hubble's law now works for the very distant galaxies where nothing else does.
那些星系同时给出距离和红移，于是哈勃常数得到了标定—— 哈勃定律从此可以用到那些别无他法可及的极遥远星系上。
Notice the dependency: an error low on the ladder propagates all the way up, which is exactly why the value of the Hubble constant is still argued over.
注意这种依赖关系：阶梯底部的一个误差会一路向上传播， 这正是哈勃常数的数值至今仍有争论的原因。
Three marks to secure.
三个要拿稳的分。
First, flux is luminosity over four pi distance squared — the inverse-square law — so a standard candle gives distance.
第一，通量等于光度除以四π距离平方——这就是平方反比定律—— 所以一个标准烛光就能给出距离。
Second, Wien's law gives temperature from the peak wavelength, and Stefan's law gives luminosity from radius and temperature.
第二，维恩定律由峰值波长给出温度， 斯特藩定律由半径和温度给出光度。
Third, redshift is the change in wavelength over wavelength, roughly speed over the speed of light, and Hubble's law links speed to distance.
第三，红移等于波长的变化除以波长， 约等于速度除以光速，而哈勃定律把速度和距离联系起来。
Master these, and the cosmos is yours.
掌握这些，宇宙就是你的了。