This lecture moves from neutrinos and the Nobel Physics Prize to the observation and evolution of stars. A short-lived observer's view of human life motivates statistical reasoning about stellar populations. Brightness, colour, distance, and binary motion lead to the Hertzsprung–Russell diagram, where star clusters reveal the stages of stellar evolution.
Neutrinos pass through ordinary matter with remarkably little interaction. Comparing their view of the world with ours introduces weakly interacting particles and leads to the historical proposal of the neutrino, motivated by missing energy in nuclear reactions.
[00:00] Before today's main lecture,
[00:04] if you are interested in science or popular science,
[00:08] you may have seen the news about the Nobel Physics Prize.
[00:13] This year, it is about neutrinos.
[00:16] What do you know about neutrinos?
[00:21] Before discussing neutrinos, think about our material world.
[00:26] Is our material world solid?
[00:31] Are solids really solid?
[00:36] What do we mean by that?
[00:38] We mean that space is occupied by something.
[00:42] When you touch it, you cannot pass through.
[00:46] You cannot pass through it when you touch it,
[00:50] and it can even make a sound.
[00:54] But can particles pass through us with almost no resistance?
[00:59] With almost no interaction?
[01:04] Yes. What particles are they?
[01:08] Neutrinos.
[01:10] And dark matter: we do not know what it is,
[01:14] but it interacts very weakly, perhaps even more weakly.
[01:18] And also gravitons.
[01:20] To these particles, the world is essentially empty.
[01:26] To us, the world looks solid.
[01:31] A piece of solid matter is occupied by atoms.
[01:35] But it is different for a neutrino.
[01:38] If you were a neutrino, you would see the world differently.
[01:43] You would see atoms arranged in a lattice,
[01:48] with tiny nuclei in that lattice.
[01:54] To a neutrino, those nuclei are extremely small.
[02:00] It passes through people and Earth almost without trouble.
[02:05] Almost without trouble.
[02:07] Every second, hundreds of trillions of neutrinos
[02:11] pass through our bodies.
[02:15] These neutrinos come from the Sun alone.
[02:19] Their interaction probability is extremely small.
[02:22] We now understand the word 'trillion' a little better,
[02:27] because of language models.
[02:29] The interaction rate is extremely small.
[02:33] That is, 99.999…% of the neutrinos
[02:38] pass through your body without any interaction.
[02:44] The same applies to Earth.
[02:46] Once I give you these numbers, you should be able
[02:52] to calculate the others by proportion.
[02:53] Water, rock, and metal are a little different,
[02:58] but not very different.
[03:01] These are the numbers passing through Earth each second.
[03:06] This is their interaction probability.
[03:09] So many neutrinos interact each second
[03:13] with matter on Earth.
[03:17] But each neutrino almost always just passes through.
[03:20] To a neutrino, Earth looks like an empty lattice.
[03:28] Whether the world is solid or empty is relative.
[03:33] It depends on which particle's perspective you take.
[03:40] When did we first understand neutrinos?
[03:44] This is interesting: neutrinos interact so weakly,
[03:50] you might imagine that people only thought
[03:54] of their existence very late. But that is not the case.
[04:00] Neutrinos were discussed in the 1930s.
[04:06] Why did people discuss neutrinos so early, in the 1930s?
[04:17] What was a main theme of physics in the 1930s?
[04:22] Quantum theory. What else, besides quantum theory?
[04:28] Nuclear physics. Yes, very good.
[04:31] Nuclear physics combines quantum theory and relativity.
[04:36] We knew of many nuclear reactions, and in some of them,
[04:42] the initial and final energies did not seem to match.
[04:49] Relativity says that energy should be conserved,
[04:54] including rest energy, mass energy, and kinetic energy.
[05:00] But they did not match. Even very famous scientists,
[05:06] such as Niels Bohr, wondered if energy was not conserved.
[05:12] But Pauli said no: it was not a failure of conservation.
[05:17] A more creative answer was that there might be
[05:22] a little particle, called a neutrino: a 'little particle'.
[05:28] It does not interact with us, so we miss it escaping.
[05:36] That was the proposal of the neutrino.
[05:40] Arguably, the neutrino was the first particle
[05:45] whose existence was predicted by theory.
[05:50] I mean an elementary particle, predicted by nuclear physics.
[05:56] That theory builds on quantum physics and relativity.
[06:01] But Dirac also predicted the positron around the same time.
[06:08] Beyond elementary particles, there are more examples.
[06:12] So neutrinos were predicted, but discovered much later.
[06:20] Their discovery came in the 1950s.
[00:00] 今天開始正式講課之前，
[00:04] 如果你對科學或科普有興趣，
[00:08] 可能已經留意到諾貝爾物理學獎的新聞。
[00:13] 今年的獎項與中微子有關。
[00:16] 你對中微子有甚麼認識？
[00:21] 談中微子之前，先想想我們的物質世界。
[00:26] 我們的物質世界是實在的嗎？
[00:31] 固體真的實在嗎？
[00:36] 這是甚麼意思？
[00:38] 我們是指空間被某些東西佔據了。
[00:42] 碰到它時，你不能穿過去。
[00:46] 碰到它時，你不能穿過去，
[00:50] 甚至還會發出聲音。
[00:54] 但有粒子能幾乎毫無阻礙地穿過我們嗎？
[00:59] 幾乎沒有任何相互作用？
[01:04] 有。它們是甚麼粒子？
[01:08] 中微子。
[01:10] 還有暗物質：我們不知道它是甚麼，
[01:14] 但它的相互作用很弱，甚至可能更弱。
[01:18] 還有引力子。
[01:20] 對這些粒子來說，世界基本上是空的。
[01:26] 在我們眼中，世界是實在的。
[01:31] 一塊固體裏面佔滿了原子。
[01:35] 但對中微子來說，情況不同。
[01:38] 如果你是中微子，看到的世界會很不一樣。
[01:43] 你會看到原子排列成晶格，
[01:48] 晶格中只有很小的原子核。
[01:54] 在中微子眼中，那些原子核非常小。
[02:00] 它幾乎毫無阻礙地穿過人體和地球。
[02:05] 幾乎沒有阻礙。
[02:07] 每秒都有數百萬億個中微子
[02:11] 穿過我們的身體。
[02:15] 這些還只是來自太陽的中微子。
[02:19] 它們發生相互作用的機率極低。
[02:22] 現在我們對「萬億」這個詞更熟悉了，
[02:27] 因為有了語言模型。
[02:29] 相互作用的發生率極低。
[02:33] 也就是說，99.999…%的中微子
[02:38] 會直接穿過人體，不發生任何相互作用。
[02:44] 對地球來說也是如此。
[02:46] 有了這些數字，你應該能夠
[02:52] 按比例計算出其他數字。
[02:53] 水、岩石和金屬會有些差別，
[02:58] 但差別並不大。
[03:01] 這些是每秒穿過地球的中微子數量。
[03:06] 這是它們的相互作用機率。
[03:09] 因此，每秒確實有很多中微子
[03:13] 與地球上的物質發生相互作用。
[03:17] 但每個中微子幾乎都只會直接穿過。
[03:20] 在中微子眼中，地球像一個空的晶格。
[03:28] 世界是實在還是空的，是相對而言的。
[03:33] 要看你是從哪種粒子的角度觀察。
[03:40] 我們甚麼時候開始認識中微子？
[03:44] 這很有趣：中微子的相互作用那麼弱，
[03:50] 你可能以為，人們到了很晚
[03:54] 才想到它們的存在，但事實並非如此。
[04:00] 早在1930年代，人們已經討論中微子。
[04:06] 為甚麼早在1930年代就開始討論中微子？
[04:17] 1930年代物理學的重要課題是甚麼？
[04:22] 量子理論。除了量子理論，還有甚麼？
[04:28] 核物理。對，很好。
[04:31] 核物理結合了量子理論和相對論。
[04:36] 我們知道很多核反應，而在其中一些反應中，
[04:42] 初始能量和最終能量似乎不相符。
[04:49] 相對論告訴我們，能量應該守恆，
[04:54] 包括靜止能量、質量能量和動能。
[05:00] 但能量不相符。當時連很著名的科學家，
[05:06] 例如尼爾斯・玻爾，也懷疑能量是否不守恆。
[05:12] 但泡利說不是，並非能量守恆失效。
[05:17] 更有創意的解釋是，可能存在
[05:22] 一種小粒子，叫中微子，意思就是「小粒子」。
[05:28] 它不與我們相互作用，所以溜走也沒被察覺。
[05:36] 這就是提出中微子的由來。
[05:40] 中微子或許可以說是第一種
[05:45] 由理論預測其存在的粒子。
[05:50] 我是指由核物理理論預測的基本粒子。
[05:56] 這套理論建立在量子物理和相對論之上。
[06:01] 不過，狄拉克也在差不多同時預測了正電子。
[06:08] 如果不只看基本粒子，還有更多例子。
[06:12] 中微子先被預測，但很久之後才被發現。
[06:20] 直到1950年代才發現它們。
The discussion places the Nobel Physics Prize in the wider history of neutrino research, then explains how IceCube turns Antarctic ice into an astronomical observatory. Secondary signals reveal energetic neutrinos, opening a new view of cosmic sources and the Milky Way.
[00:00] Coming back to the Nobel Prize,
[00:04] many Nobel Prizes have already gone to neutrino physics.
[00:11] A lot of prizes for this little particle, including
[00:19] the 1960s discovery of the muon neutrino.
[00:24] Particles come in generations: first, the electron;
[00:30] second, the muon; third, the tau.
[00:33] Likewise, electron, muon and tau neutrinos.
[00:37] So this was the discovery of the muon neutrino.
[00:40] There were also reactor antineutrinos,
[00:44] solar neutrinos and supernova neutrinos.
[00:48] These show the years the Nobel Prizes were awarded
[00:52] and when the work was done.
[00:55] More recently, there was neutrino oscillation.
[01:00] That received a Nobel Prize. This year, it is IceCube.
[01:05] We are going beyond understanding neutrinos themselves,
[01:12] using them as a tool to understand our universe.
[01:17] You may remember from our lectures,
[01:21] or have forgotten after the quiz, that we discussed telescopes.
[01:27] We discussed telescopes beyond optical telescopes:
[01:30] neutrino telescopes and gravitational-wave telescopes.
[01:35] I did not give many examples of neutrino telescopes,
[01:39] but this is an outstanding example.
[01:43] I did mention supernova neutrinos, which are a different type.
[01:48] Here, extremely high-energy neutrinos from the cosmos
[01:52] give us an opportunity to understand
[01:56] the mysteries of the cosmos.
[02:01] Yesterday, I was watching the live broadcast.
[02:06] When they said 'ghost particles in our universe',
[02:12] I immediately realised they meant neutrinos.
[02:16] Once I knew the prize was going to neutrino research,
[02:20] I first thought of the Daya Bay experiment.
[02:24] The Daya Bay experiment measures
[02:30] the mixing angle theta 13:
[02:34] mixing between the first and third neutrinos.
[02:37] It is nonzero, and they measured its value.
[02:40] That describes how these neutrinos mix.
[02:43] If you asked me,
[02:46] 'This year's Nobel Prize is for neutrinos;
[02:50] guess who will get it?' I would have said Daya Bay.
[02:55] People usually identify two leaders of the experiment:
[03:00] Yifang Wang and Kam-Biu Luk.
[03:04] You know Kam-Biu Luk, our professor at HKUST.
[03:08] Unfortunately, the prize did not go to this experiment.
[03:12] They also gave it to only one person.
[03:14] Usually, a Nobel Prize can go to up to three people.
[03:17] But that is the reality.
[03:21] Now, back to IceCube.
[03:27] IceCube is a different kind of experiment.
[03:29] It is not measuring basic neutrino parameters,
[03:33] but counting neutrinos and looking at the sky.
[03:35] What events can produce extremely high-energy neutrinos
[03:39] that reach the Earth?
[03:43] Their interaction rate differs from our earlier estimate.
[03:49] Nevertheless, their interactions are still extremely weak.
[03:54] We need a huge volume to catch these neutrinos.
[03:58] How do we get such a huge volume?
[04:02] The brilliant idea is to go to the South Pole.
[04:05] The South Pole has a lot of ice.
[04:10] Take a cube of ice with a volume of one cubic kilometre.
[04:16] and put detectors into it.
[04:19] Then you can use that whole volume as a detector.
[04:25] What the detector sees directly are photons.
[04:29] Those photons are secondary signals.
[04:34] Neutrinos collide with matter and, for example, create muons.
[04:39] But still, modern experiments can reconstruct
[04:44] the neutrino's properties from this cascade decay,
[04:48] and identify the neutrino events.
[04:53] That is the amazing thing IceCube can do.
[04:58] It is not seeing neutrinos directly.
[05:01] Most experiments do not see neutrinos directly.
[05:05] Instead, they use a huge amount of matter.
[05:08] Neutrinos interact with it and eventually emit photons,
[05:11] or other particles that are easier to see.
[05:14] We observe those particles.
[05:17] An event usually looks like this:
[05:21] more visible particles, like muons and photons, follow a path.
[05:26] From their detection, researchers work out
[05:31] the properties of the neutrinos.
[05:36] After detecting them, they point back to sources in the sky.
[05:41] We can understand those sources better.
[05:46] The idea behind IceCube is now being applied
[05:51] to many other detectors being built.
[05:56] For example, China has projects in the South China Sea:
[06:01] the TRIDENT and HUNT detectors.
[06:04] These use seawater, not ice.
[06:07] Each dot represents a string of detectors.
[06:11] Not a single detector, but a whole string.
[06:14] This plane is the sea level,
[06:18] and each dot is a detector string.
[06:20] There is a huge number of detectors in a large array.
[06:25] IceCube was one kilometre across;
[06:28] here, this scale is 500 metres. It is a huge array.
[06:33] You can collect a great number of signals.
[06:37] There is also the next generation of IceCube,
[06:41] and many other experiments forming a global network.
[06:46] We previously discussed global networks.
[06:49] What are their advantages? Do you remember?
[06:56] First, they can cross-check their results,
[07:00] and better locate events
[07:04] by coordinating their detection times.
[07:07] It is not only about having more volume.
[07:09] By using the size of the Earth,
[07:12] we can learn much more.
[07:15] This works alongside traditional cosmic-ray detection.
[07:20] For example, take a large area of land
[07:23] and detect cascade decays from cosmic-ray particles.
[07:29] Taken together, cosmic rays,
[07:34] especially their neutrino component,
[07:40] form a great telescope for understanding the sky,
[07:43] revealing things we have never seen before.
[07:48] Do you remember these figures from our lectures?
[07:53] They show the Milky Way in different optical bands.
[07:56] There is also an image of the Milky Way seen in neutrinos.
[08:02] That image comes from IceCube.
[08:06] In future, the resolution will improve,
[08:10] showing more clearly what the Milky Way looks like
[08:14] through the eyes of neutrinos.
[08:17] Neutrinos also give us a lot of information
[08:22] about active galactic centres.
[08:27] We will return to that when we discuss galaxies.
[08:31] There are also extremely high-energy events
[08:35] whose origins we still do not understand.
[08:41] That is the story of neutrinos.
[00:00] 說回諾貝爾獎，
[00:04] 中微子物理學已獲得多次諾貝爾獎。
[00:11] 這小粒子獲獎不少，其中包括
[00:19] 1960年代發現的μ中微子。
[00:24] 粒子有不同的世代：第一代是電子，
[00:30] 第二代是μ子，第三代是τ子。
[00:33] 中微子也分為電子、μ和τ中微子。
[00:37] 這就是μ中微子的發現。
[00:40] 另外還有反應堆反中微子，
[00:44] 太陽中微子和超新星中微子。
[00:48] 這裏列出了各次諾貝爾獎的頒獎年份，
[00:52] 以及研究完成的年份。
[00:55] 較近期的則是中微子振盪。
[01:00] 這也獲得了諾貝爾獎。今年則是IceCube。
[01:05] 我們不再只是了解中微子本身，
[01:12] 而是用它們作工具，了解宇宙。
[01:17] 你們可能還記得之前的課堂內容，
[01:21] 或測驗後已忘了：我們談過望遠鏡。
[01:27] 除了光學望遠鏡，我們還談過
[01:30] 中微子望遠鏡和引力波望遠鏡。
[01:35] 當時沒有舉很多中微子望遠鏡的例子，
[01:39] 但這就是一個出色的例子。
[01:43] 我曾提過超新星中微子，那是另一類。
[01:48] 這些來自宇宙的極高能中微子，
[01:52] 讓我們有機會了解
[01:56] 宇宙的奧秘。
[02:01] 昨天我在看頒獎的直播。
[02:06] 當他們說到「宇宙中的幽靈粒子」，
[02:12] 我立即意識到他們指的是中微子。
[02:16] 知道獎項頒給中微子研究後，
[02:20] 我首先想到大亞灣實驗。
[02:24] 大亞灣實驗量度的是
[02:30] 混合角θ₁₃：
[02:34] 第一和第三種中微子之間的混合。
[02:37] 它不為零，而實驗量度了其數值。
[02:40] 這描述了這些中微子如何混合。
[02:43] 如果你問我：
[02:46] 「今年諾貝爾獎頒給中微子研究，
[02:50] 猜誰會得獎？」我會說大亞灣。
[02:55] 人們通常會提到實驗的兩位領袖：
[03:00] 王貽芳和陸錦標。
[03:04] 陸錦標是我們科大的教授。
[03:08] 可惜，獎項沒有頒給這個實驗。
[03:12] 而且只頒給一個人。
[03:14] 諾貝爾獎通常最多可由三人分享。
[03:17] 但結果就是這樣。
[03:21] 現在說回IceCube。
[03:27] IceCube是另一類實驗。
[03:29] 它不是量度中微子的基本參數，
[03:33] 而是觀測中微子的數量和天空。
[03:35] 哪些事件會產生極高能中微子，
[03:39] 並讓它們到達地球？
[03:43] 它們的相互作用率與之前的估算不同。
[03:49] 但它們的相互作用仍然極弱。
[03:54] 所以需要極大的體積來捕捉中微子。
[03:58] 怎樣取得這麼大的體積？
[04:02] 一個巧妙的構想是到南極。
[04:05] 南極有大量的冰。
[04:10] 取一個體積為一立方公里的冰塊，
[04:16] 把探測器放進去。
[04:19] 整個體積就可用作探測器。
[04:25] 探測器直接看到的是光子。
[04:29] 這些光子是次級訊號。
[04:34] 中微子與物質碰撞，例如產生μ子。
[04:39] 但現代實驗仍能根據
[04:44] 這一連串衰變重建中微子的性質，
[04:48] 並識別中微子事件。
[04:53] 這就是IceCube能做到的驚人之處。
[04:58] 它並非直接看到中微子。
[05:01] 大部分實驗都不是直接看到中微子。
[05:05] 它們使用大量的物質。
[05:08] 中微子與之作用，最終產生光子，
[05:11] 或其他較容易觀測的粒子。
[05:14] 我們觀測的是這些粒子。
[05:17] 一個事件通常是這樣的：
[05:21] μ子、光子等較易觀測的粒子沿軌跡移動。
[05:26] 研究人員從探測到的訊號，
[05:31] 推斷中微子的性質。
[05:36] 探測到它們後，便追溯天空中的來源。
[05:41] 這樣就能更了解那些天體。
[05:46] IceCube背後的構想，現在也用於
[05:51] 許多正在建造的探測器。
[05:56] 例如，中國在南海有一些項目：
[06:01] TRIDENT和HUNT探測器。
[06:04] 它們使用海水，而不是冰。
[06:07] 每個點代表一串探測器。
[06:11] 不是單一探測器，而是一整串。
[06:14] 這個平面是海面，
[06:18] 每個點則是一串探測器。
[06:20] 大型陣列中有大量探測器。
[06:25] IceCube的尺度是一公里；
[06:28] 這裏的尺度是500米，也是大型陣列。
[06:33] 因此可以收集大量訊號。
[06:37] 此外還有下一代IceCube，
[06:41] 以及許多實驗，組成全球網絡。
[06:46] 之前我們談過全球網絡。
[06:49] 你們記得這種網絡有甚麼好處嗎？
[06:56] 首先，可以互相核對結果，
[07:00] 並更準確地確定事件的位置，
[07:04] 方法是協調各地的探測時間。
[07:07] 不只是增加探測的體積，
[07:09] 還利用地球的尺度，
[07:12] 來獲得更多資訊。
[07:15] 再配合傳統的宇宙射線探測方法。
[07:20] 例如，在一大片地面上
[07:23] 探測宇宙射線粒子的一連串衰變。
[07:29] 綜合起來，宇宙射線，
[07:34] 尤其當中的中微子，
[07:40] 就成為了解天空的強大望遠鏡，
[07:43] 讓我們看到前所未見的事物。
[07:48] 記得之前課堂中的這些圖嗎？
[07:53] 它們顯示不同光學波段中的銀河系。
[07:56] 也有用中微子觀測的銀河系影像。
[08:02] 那幅影像由IceCube提供。
[08:06] 將來影像的解像度會更高，
[08:10] 讓我們更清楚看到銀河系
[08:14] 在中微子眼中的模樣。
[08:17] 中微子也提供了很多關於
[08:22] 活躍星系中心的資訊。
[08:27] 談到星系時，我們會再討論這一點。
[08:31] 還有一些極高能事件，
[08:35] 其來源至今仍未明白。
[08:41] 這就是中微子的故事。
A short-lived fly observing people provides an analogy for studying stars whose lifetimes far exceed ours. Comparing people of similar ages shows why size differences cannot simply be interpreted as age differences, and motivates the study of groups of stars born together.
[00:00] What interesting questions would we like to ask about stars?
[00:06] Previously, we talked about our Solar System.
[00:10] The Solar System is a system led by a star.
[00:13] It is especially interesting because it can support human life,
[00:19] which seems to be very rare.
[00:21] Now let us talk about stars, objects like the Sun.
[00:25] What are we interested in about stars?
[00:30] First, rather than just imagining, we rely on observations
[00:35] to understand the main properties of stars.
[00:38] What kinds of observations can we make?
[00:41] Last time, we asked you to think about the major challenge
[00:47] in making these observations.
[00:51] What is the major challenge?
[00:53] The major challenge is that our lifetimes are too short.
[00:58] It is like a fly trying to study humans.
[01:05] Imagine a very smart fly that can do many things,
[01:10] but still lives only a short time, perhaps one month.
[01:15] How can this fly understand the nature of humans?
[01:20] For example, how can it understand human growth?
[01:26] What do I mean by human growth?
[01:28] The fly sees infants and very young children.
[01:35] They are very short.
[01:38] It also sees adults, who are relatively taller.
[01:42] Naturally, the fly can understand
[01:46] that an infant can grow into an adult.
[01:50] But how general is this conclusion?
[01:53] Can a short adult grow into a taller adult?
[02:00] For example, the fly sees someone like Yao Ming.
[02:06] If I live long enough, can I grow as tall as Yao Ming?
[02:11] How could the fly answer this question just by observing?
[02:17] How could it answer this question?
[02:27] Is being short or tall simply a matter of time to grow?
[02:33] Or are there other factors?
[02:47] Let us say the fly can see a great many humans.
[02:50] It is very smart and can fly very fast.
[02:54] It observes humans here and there.
[02:57] It can observe millions, or even a billion people,
[03:02] perhaps every human in the world.
[03:05] How can it decide whether a short adult can become taller?
[03:11] Can a short adult grow into a tall adult?
[03:29] Some structures in human society
[03:33] can help us answer this question. What structures?
[03:36] For example, this class. Why is this class helpful?
[03:41] Most of you are roughly the same age.
[03:46] The fly immediately sees people of roughly the same age,
[03:50] whose heights are still different.
[03:56] The difference is not only due to the time
[04:02] we have had to grow.
[04:04] It can also observe some alumni.
[04:09] For example, alumni who entered HKUST when it first opened
[04:15] come back to HKUST to celebrate its anniversary.
[04:21] The fly observes these people.
[04:25] Statistically, they are not taller or shorter than you.
[04:32] So differences in height are not only due to age.
[04:37] There are other kinds of variation.
[04:43] The key is to identify a group of people
[04:48] who are roughly the same age.
[04:54] Why do I say this? Think about stars.
[04:58] How can we identify a group of stars of similar age?
[05:03] That will greatly help us understand the nature of stars.
[05:09] That is one question.
[00:00] 關於恆星，我們想問哪些有趣的問題？
[00:06] 之前我們談過太陽系。
[00:10] 太陽系是以一顆恆星為中心的系統。
[00:13] 它特別有趣，因為有適合人類生存的條件，
[00:19] 而這種條件似乎很罕見。
[00:21] 現在我們來談像太陽這樣的恆星。
[00:25] 我們對恆星的哪些事情感興趣？
[00:30] 首先，我們不只憑想像，而是依靠觀測，
[00:35] 去了解恆星的主要性質。
[00:38] 我們可以進行甚麼觀測？
[00:41] 上次我們請大家思考觀測恆星的主要挑戰，
[00:47] 究竟在觀測時會遇到甚麼困難。
[00:51] 最大的挑戰是甚麼？
[00:53] 最大的挑戰是我們的壽命太短。
[00:58] 這就像一隻蒼蠅試圖研究人類。
[01:05] 想像一隻很聰明、能做很多事的蒼蠅，
[01:10] 但牠壽命仍然很短，例如只有一個月。
[01:15] 這隻蒼蠅如何了解人類的性質？
[01:20] 例如，牠如何了解人類的成長？
[01:26] 我說的人類成長是甚麼意思？
[01:28] 蒼蠅看到嬰兒和年幼的小孩。
[01:35] 他們都很矮小。
[01:38] 牠也看到比較高的成年人。
[01:42] 很自然地，蒼蠅可以理解，
[01:46] 嬰兒可以長大成為成年人。
[01:50] 但這個結論能推廣到甚麼程度？
[01:53] 一個矮的成年人能繼續長高嗎？
[02:00] 例如，蒼蠅看到姚明那麼高的人。
[02:06] 如果我活得夠久，能長到姚明那麼高嗎？
[02:11] 蒼蠅如何只憑觀察回答這個問題？
[02:17] 牠如何找出答案？
[02:27] 高矮是否只取決於成長的時間？
[02:33] 還是有其他因素？
[02:47] 假設蒼蠅能看到很多人。
[02:50] 牠很聰明，而且飛得很快。
[02:54] 牠到處觀察人類。
[02:57] 牠可以觀察數百萬，甚至十億人，
[03:02] 甚至世界上的每一個人。
[03:05] 牠如何判斷矮的成年人能否繼續長高？
[03:11] 矮的成年人能長成高的成年人嗎？
[03:29] 人類社會中的一些結構，
[03:33] 能幫助我們回答這個問題。是甚麼結構？
[03:36] 例如這個班級。它為甚麼特別有用？
[03:41] 你們大多數人的年齡相近。
[03:46] 蒼蠅立即看到一群年齡相近的人，
[03:50] 但他們的身高仍然不同。
[03:56] 這些差異不只是因為，
[04:02] 我們有多少時間長大。
[04:04] 牠還可以觀察一些校友。
[04:09] 例如在科大剛創立時入學的校友，
[04:15] 回到科大參加校慶。
[04:21] 蒼蠅觀察這些人。
[04:25] 從統計上看，他們並不比你們高或矮。
[04:32] 所以身高的差異不只取決於年齡。
[04:37] 還有其他因素造成的差異。
[04:43] 關鍵是找出一群人，
[04:48] 他們的年齡大致相同。
[04:54] 我為甚麼這樣說？想想恆星。
[04:58] 我們如何找出一群年齡相近的恆星？
[05:03] 這能大大幫助我們了解恆星的性質。
[05:09] 這是其中一個問題。
Population counts can reveal how long a typical object spends in different stages of life. The fly analogy illustrates this reasoning, while a discussion of selection bias explains why the objects we can detect may not represent the whole population.
[00:00] Another question: after seeing many individuals,
[00:05] the fly can identify adults
[00:10] whose heights are roughly constant.
[00:16] Their heights stay about the same.
[00:19] Then it finds that there are more adults.
[00:23] Most people are adults rather than children or infants.
[00:28] There are more adults than children. What can it conclude?
[00:33] What does the fly conclude from seeing more adults?
[00:38] (Student) It is difficult to observe the children.
[00:46] Let us assume it can observe the children.
[00:50] The fly is so capable that it observes every person
[00:55] in the world.
[00:58] You raise a very good point: there could be selection bias.
[01:05] Selection bias also exists in astronomy. Some stars are too faint.
[01:10] They are not bright enough for us to see.
[01:12] If we are like the fly, we have a bias
[01:16] because we study only the stars that we can see.
[01:20] That is a very good point, but I mean something different.
[01:24] Even if the fly can see everyone in the world,
[01:29] it still sees more adults than children.
[01:32] What can it conclude?
[01:37] The immediate conclusion is simply
[01:42] that there are more adults than children in the world.
[01:46] That is roughly true, unless there is some disaster.
[01:50] For example, Liu Cixin's science-fiction novel Supernova Era.
[01:56] In Supernova Era, a disaster such as a supernova explosion
[02:02] kills many more adults than children, or something like that.
[02:06] But apart from such cases, imagine a normal world
[02:13] where there are more adults than children.
[02:19] What does this tell the fly about any one individual,
[02:24] any individual human being?
[02:27] What conclusion can the fly draw?
[02:39] There is an interplay between space and time.
[02:42] The fly sees different people in different places.
[02:45] Now consider one individual, assuming this person is typical.
[02:51] The fly can infer that, over this person's whole life,
[02:57] more time is spent as an adult than as a child.
[03:05] Seeing more adults than children means that a typical person
[03:09] spends more time in adulthood than in childhood.
[03:15] This is also a very important lesson for understanding stars.
[03:20] There is a particularly important family of stars
[03:24] called main-sequence stars.
[03:27] We will see how a star enters the main sequence
[03:33] as it goes from childhood to adulthood, so to speak.
[03:38] Eventually, when a star gets old or dies,
[03:44] depending on how we define death, it leaves the main sequence.
[03:48] In our Universe, we see more main-sequence stars.
[03:52] Even though our lives are very short compared with stars,
[03:56] we can understand that a typical star spends
[04:01] most of its lifetime on the main sequence.
[04:05] I will return to this point later.
[04:08] The common-sense approach of a fly observing humans
[04:14] applies directly to how we understand stars.
[04:20] This example comes from the book 100 Billion Suns:
[04:25] The Birth, Life, and Death of the Stars.
[04:28] It is a brilliant popular-science book.
[04:31] I think it was originally written in German.
[04:34] There are English and Chinese translations.
[04:37] If you are interested, I strongly encourage you to read it.
[00:00] 另一個問題：觀察很多個人之後，
[00:05] 蒼蠅能辨認出成年人，
[00:10] 他們的身高大致保持不變。
[00:16] 他們的身高不再明顯改變。
[00:19] 接着牠發現成年人比較多。
[00:23] 大多數人是成年人，而不是兒童或嬰兒。
[00:28] 成年人比兒童多。牠能得出甚麼結論？
[00:33] 看到更多成年人，蒼蠅能得出甚麼結論？
[00:38] （同學）小孩可能比較難觀察到。
[00:46] 假設牠也能觀察到小孩。
[00:50] 這隻蒼蠅很厲害，能觀察每一個人，
[00:55] 包括全世界的所有人。
[00:58] 你提出了很好的觀點：可能有選擇偏差。
[01:05] 天文學也有選擇偏差：有些恆星太暗。
[01:10] 它們不夠亮，我們看不到。
[01:12] 如果我們像蒼蠅一樣，也會有偏差，
[01:16] 因為我們只研究看得到的恆星。
[01:20] 這是很好的觀點，但我指的是另一回事。
[01:24] 即使蒼蠅能看到世界上的每一個人，
[01:29] 牠仍看到成年人比兒童多。
[01:32] 牠能得出甚麼結論？
[01:37] 直接的結論就是，
[01:42] 世界上的成年人比兒童多。
[01:46] 這大致正確，除非發生某種災難。
[01:50] 例如劉慈欣的科幻小說《超新星紀元》。
[01:56] 《超新星紀元》中發生超新星爆發等災難，
[02:02] 造成的成年人死亡遠多於兒童。
[02:06] 除了這類情況，想像一個正常的世界，
[02:13] 成年人比兒童多。
[02:19] 這能讓蒼蠅了解任何一個個體，
[02:24] 任何一個人的甚麼事情？
[02:27] 蒼蠅能得出甚麼結論？
[02:39] 這裏有空間與時間的相互關係。
[02:42] 蒼蠅在不同地方看到不同的人。
[02:45] 現在考慮一個人，假設他是典型的個體。
[02:51] 蒼蠅可以推斷，在這個人的一生中，
[02:57] 他當成年人的時間比當兒童的時間長。
[03:05] 成年人比兒童多，意味着對典型的人來說，
[03:09] 成年期比童年期長。
[03:15] 這也是了解恆星的一個重要啟示。
[03:20] 有一類特別重要的恆星，
[03:24] 稱為主序星。
[03:27] 我們稍後會看到恆星如何進入主序階段，
[03:33] 可以說是從童年成長為成年。
[03:38] 最後，當恆星變老或死亡時，
[03:44] 視乎我們如何定義死亡，它會離開主序階段。
[03:48] 在宇宙中，我們看到的主序星比較多。
[03:52] 即使我們的壽命遠比恆星短，
[03:56] 我們仍能知道，一顆典型恆星會，
[04:01] 在主序階段度過一生中的大部分時間。
[04:05] 我稍後會再談這一點。
[04:08] 蒼蠅觀察人類的這種常識方法，
[04:14] 可以直接用來理解恆星。
[04:20] 這個例子出自《千億個太陽》這本書：
[04:25] 副題是「恆星的誕生、生命與死亡」。
[04:28] 這是一本精彩的科普書。
[04:31] 我想它的原文是德文。
[04:34] 也有英文和中文譯本。
[04:37] 如果你有興趣，我很鼓勵你讀這本書。
A student's question tests the assumptions behind the fly analogy. The response brings together evidence for stellar birth and death, including star-forming regions, a finite cosmic history, nuclear fuel, supernovae, and stellar remnants.
[00:01] The fly concludes that human adulthood lasts longer, right?
[00:09] But that assumes the fly understands the concept…
[00:15] We are comparing flies with humans,
[00:20] just as we compare humans with stars.
[00:25] We need to know that a star can grow and die,
[00:29] just as the fly needs to know
[00:34] that a human can grow and die.
[00:38] But the fly's life is too short
[00:42] to observe a person growing and dying.
[00:45] How does it know that people can grow and die?
[00:47] This is a brilliant question. How do we know?
[00:50] First, what I am saying is based on an assumption:
[00:54] a star is not there forever.
[01:00] It is born at some time
[01:04] and eventually dies.
[01:08] That may be hard to see in a single observation.
[01:13] But we can understand stellar birth and death
[01:19] from many other things.
[01:20] For example, looking far away means looking into the past.
[01:27] In earlier eras, we find more stars being born
[01:34] and nebulae turning into stars.
[01:37] We cannot follow the entire process for one star:
[01:41] the dynamical process takes too long.
[01:44] But we see many similar places where stars are born.
[01:50] We also know that the age of the universe is finite.
[01:57] Stars cannot have been there forever.
[02:00] The earliest stars began shining surprisingly early,
[02:04] within a billion years of the universe's birth.
[02:11] Still, there must have been an initial time
[02:17] when the stars were born.
[02:20] We know stars are supported by nuclear reactions.
[02:24] Eventually they run out of fuel and die.
[02:29] We do see stellar deaths, including supernova explosions
[02:35] and events such as the formation of white dwarfs.
[02:41] Supernova explosions are especially bright.
[02:44] We observe many supernova explosions
[02:50] in modern astronomy.
[02:52] In ancient China, people carefully recorded the sky,
[02:59] especially transient events.
[03:03] A transient event could be a star
[03:07] that suddenly becomes very bright.
[03:13] A supernova was recorded in the Song Dynasty.
[03:17] Astronomers now find a nebula there,
[03:22] the remnant of that supernova explosion.
[03:26] Although an individual human life is short,
[03:31] these extremely rapid, transient events
[03:35] can still be understood from human history.
[03:38] You raise a very good point: this is a simplified story.
[03:43] Our comprehensive understanding of everything
[03:47] is what makes the story reliable.
[03:50] Without going into great technical detail,
[03:54] I am trying to explain that reliable story understandably.
[04:00] You are very much encouraged to ask deeper questions
[04:04] and see how we really understand these things.
[04:08] So that was the analogy.
[00:01] 蒼蠅推斷人類成年期較長，對嗎？
[00:09] 但這要蒼蠅明白相關概念……
[00:15] 我們把蒼蠅與人類作比較，
[00:20] 就像把人類與恆星作比較。
[00:25] 我們要知道恆星會成長和死亡，
[00:29] 就像蒼蠅需要知道，
[00:34] 人類會成長和死亡。
[00:38] 但蒼蠅的壽命太短，
[00:42] 無法觀察人類的成長和死亡。
[00:45] 牠怎樣知道人類會成長和死亡？
[00:47] 這問題很精彩。我們怎樣知道呢？
[00:50] 首先，我的說法建基於一個假設：
[00:54] 恆星並非永遠存在。
[01:00] 它在某個時刻誕生，
[01:04] 並最終死亡。
[01:08] 單次觀測或許很難看出這一點。
[01:13] 但我們可以理解恆星的誕生與死亡，
[01:19] 透過許多其他證據。
[01:20] 例如，觀察遠方就是觀察過去。
[01:27] 在較早的時代，我們看到更多恆星誕生，
[01:34] 也看到星雲形成恆星。
[01:37] 我們無法跟進一顆恆星的完整過程：
[01:41] 其演化過程需時太長。
[01:44] 但我們看到許多類似的恆星誕生區域。
[01:50] 我們也知道宇宙的年齡是有限的。
[01:57] 恆星不可能一直存在。
[02:00] 最早的恆星很早就開始發光，
[02:04] 在宇宙誕生後十億年內便已出現。
[02:11] 不過，它們必定有一個起點，
[02:17] 也就是恆星誕生的時刻。
[02:20] 我們知道恆星由核反應支撐。
[02:24] 它們最終會耗盡燃料並死亡。
[02:29] 我們確實看到恆星死亡，例如超新星爆炸，
[02:35] 以及白矮星形成等現象。
[02:41] 超新星爆炸尤其明亮。
[02:44] 我們觀測到許多超新星爆炸，
[02:50] 在現代天文學中。
[02:52] 古代中國的人仔細記錄天空，
[02:59] 尤其留意暫現事件。
[03:03] 暫現事件可以是一顆恆星，
[03:07] 突然變得非常明亮。
[03:13] 宋代曾記錄過一次超新星。
[03:17] 現在天文學家在該處找到星雲，
[03:22] 那是超新星爆炸的遺跡。
[03:26] 雖然一個人的壽命很短，
[03:31] 這些極快、短暫的事件，
[03:35] 仍可透過歷史記錄加以了解。
[03:38] 你說得很好：這裏的解釋是簡化的。
[03:43] 我們對各方面的綜合理解，
[03:47] 才令這套解釋可靠。
[03:50] 這裏不深入技術細節，
[03:54] 而是嘗試用易明的方式解釋。
[04:00] 我非常鼓勵大家提出更深入的問題，
[04:04] 看看我們究竟怎樣理解這些事情。
[04:08] 以上就是這個類比。
Colour, brightness, position, and variation with time are direct clues available to astronomers. The discussion distinguishes these observations from inferred properties, using parallax to show how positional measurements can provide stellar distances.
[00:00] From the analogy, we now turn to astronomical observations.
[00:05] What kinds of observations can we make?
[00:10] We would like to do several things. First, observation.
[00:14] Find out what we can observe, then classify the stars.
[00:19] Assume only that stars are born, evolve and die.
[00:25] How can we classify stars from observation
[00:29] with minimal knowledge of a stellar model?
[00:34] Afterwards, we will model the underlying physical processes:
[00:40] how stars are born, burn and eventually die.
[00:47] We do this at different levels.
[00:51] For the same thing, there are different ways to reason.
[00:58] We can understand it through observations and statistics,
[01:02] and through the underlying first principles.
[01:07] Now, the first question: what can we observe about stars?
[01:15] Using modern telescopes, what are the main observables?
[01:19] What can we observe about stars?
[01:22] Any ideas? What can our telescopes observe about stars?
[01:30] Colour. Very good.
[01:32] A star's colour is basically the frequency of its light.
[01:36] Even our phones can distinguish different colours.
[01:43] Modern telescopes use photometry and spectroscopy.
[01:48] Spectroscopic telescopes see many channels,
[01:52] making detailed measurements in many frequency bands.
[01:59] They measure colour much more carefully than we do.
[02:02] Our eyes only see three colours.
[02:05] Colour is great. Anything else?
[02:16] Distance is not a direct observable.
[02:19] Measuring distance carefully is a major astronomy challenge.
[02:26] It is indirect. Apart from colour, what can we see directly?
[02:35] Brightness. Very good.
[02:37] Colour and brightness are the most important observables.
[02:42] We can also talk about where the star is.
[02:48] Its position is not an intrinsic property of the star,
[02:52] but it can help us do statistics.
[02:57] Changes over time are also interesting observables.
[03:01] Most stars do not change very significantly over time.
[03:05] But some variable stars give us more information.
[03:10] Those changes interest us too.
[03:13] As mentioned, distance is not directly observable.
[03:17] We can use parallax observations
[03:23] to understand stars that are relatively nearby
[03:27] and measure their distances.
[03:32] By the way, what is the fundamental observable in parallax?
[03:40] The fundamental observable we see
[03:45] is actually position. That is directly observable.
[03:49] From position, we derive distance,
[03:52] if the star is not very far away.
[03:56] Let's start with the brightness of stars.
[04:00] For stellar brightness…
[00:00] 從這個類比，我們轉到天文觀測。
[00:05] 我們可以進行甚麼觀測？
[00:10] 我們想做幾件事，首先是觀測。
[00:14] 先找出可觀測的量，再將恆星分類。
[00:19] 只假設恆星會誕生、演化和死亡。
[00:25] 如何單靠觀測把恆星分類，
[00:29] 而只需很少的恆星模型知識？
[00:34] 然後，我們建立基本物理過程的模型：
[00:40] 恆星如何誕生、燃燒，並最終死亡。
[00:47] 我們從不同層面研究。
[00:51] 同一件事，可以用不同方式理解和推理。
[00:58] 我們可透過觀測和統計來理解，
[01:02] 也可從背後的基本原理來理解。
[01:07] 首先，我們可以觀測恆星的甚麼？
[01:15] 用現代望遠鏡，主要可觀測的量是甚麼？
[01:19] 我們可以觀測恆星的甚麼？
[01:22] 有甚麼想法？望遠鏡能觀測恆星的甚麼？
[01:30] 顏色。很好。
[01:32] 恆星的顏色基本上就是光的頻率。
[01:36] 連手機也能分辨不同顏色。
[01:43] 現代望遠鏡使用測光和光譜觀測。
[01:48] 光譜望遠鏡能看到很多頻道，
[01:52] 詳細量度不同頻段的光。
[01:59] 它們量度顏色，比我們細緻得多。
[02:02] 我們的眼睛只看到三種顏色。
[02:05] 顏色很好。還有甚麼？
[02:16] 距離不是直接可觀測的量。
[02:19] 準確量度距離是天文學的一大挑戰。
[02:26] 它是間接量。除了顏色，還能直接看到甚麼？
[02:35] 亮度。很好。
[02:37] 顏色和亮度是最重要的可觀測量。
[02:42] 我們也可以說恆星在哪裏。
[02:48] 位置不是恆星的內在性質，
[02:52] 但有助我們進行統計。
[02:57] 隨時間的變化也是有趣的可觀測量。
[03:01] 大部分恆星隨時間的變化不太明顯。
[03:05] 但某些變星能提供更多資訊。
[03:10] 我們也關注這些變化。
[03:13] 正如剛才所說，距離無法直接觀測。
[03:17] 我們可以透過視差觀測，
[03:23] 了解較近的恆星，
[03:27] 並量度它們的距離。
[03:32] 順帶一提，視差觀測最基本的量是甚麼？
[03:40] 我們直接觀測到的基本量，
[03:45] 其實是位置。位置可直接觀測。
[03:49] 我們由位置推算距離，
[03:52] 只要恆星不是太遠。
[03:56] 我們先從恆星的亮度開始。
[04:00] 關於恆星的亮度……
Apparent magnitude describes how bright a star looks from Earth, while absolute magnitude compares stars at a common distance of ten parsecs. The logarithmic magnitude scale makes it easier to discuss brightness across an enormous range.
[00:00] A common measure of brightness is apparent magnitude.
[00:07] A star's apparent magnitude is defined by this formula.
[00:13] It uses a logarithm of the flux, with a reference flux.
[00:19] Magnitude minus reference magnitude is a logarithm
[00:25] of flux divided by reference flux.
[00:28] More negative means brighter.
[00:33] The Sun's apparent magnitude is around minus 30.
[00:37] The Moon is around minus 10.
[00:40] The brightest star in the sky is roughly minus one.
[00:45] The famous star Vega is about zero.
[00:50] Our eyes can see down to roughly magnitude six
[00:55] under very good observing conditions.
[01:01] Apparent magnitude is the brightness we directly see.
[01:06] There is also absolute magnitude.
[01:09] Apparent magnitude depends on two things.
[01:11] One is how bright the star is in itself.
[01:16] The other is how far away it is.
[01:19] If it is far away, it looks less bright.
[01:22] Absolute magnitude describes its intrinsic brightness.
[01:28] It is the apparent magnitude at a distance of 10 parsecs.
[01:35] We discussed parsecs: one is roughly three light-years.
[01:41] So 10 parsecs is about 30 light-years,
[01:44] around the distance of this star.
[01:49] That is how we describe a star's brightness.
[01:52] Now think: why define magnitude using a logarithm?
[01:59] Why use a logarithm?
[02:05] Why use logarithms to define stellar brightness?
[02:10] Why is that easier than talking directly about flux?
[02:20] Because you represent the light...
[02:23] Why is it easier?
[02:26] The light can be very large, right?
[02:29] Yes. In that respect, it is very difficult.
[02:31] Yes, very good. Both brightness and distance matter.
[02:37] Even distances can vary enormously, from the Sun
[02:43] to near the edge of our observable universe.
[02:47] The numbers are extremely different.
[02:50] It is easier to show them using logarithms.
[00:00] 亮度常用的量度是視星等。
[00:07] 恆星的視星等由這條公式定義。
[00:13] 它用通量的對數，並有參考通量。
[00:19] 星等減去參考星等，等於一個對數，
[00:25] 其中是通量與參考通量的比值。
[00:28] 星等越負，表示越光亮。
[00:33] 太陽的視星等大約是負三十。
[00:37] 月亮大約是負十。
[00:40] 天空最亮的恆星大約是負一。
[00:45] 著名的織女星大約是零。
[00:50] 肉眼大約可以看到六等星，
[00:55] 但需要非常好的觀測條件。
[01:01] 視星等表示我們直接看到的亮度。
[01:06] 另外還有絕對星等。
[01:09] 視星等取決於兩件事。
[01:11] 第一是恆星本身有多光亮。
[01:16] 第二是它離我們有多遠。
[01:19] 離得越遠，看起來就越暗。
[01:22] 絕對星等描述它本身的亮度。
[01:28] 就是放在十秒差距時的視星等。
[01:35] 我們講過秒差距：大約等於三光年。
[01:41] 所以十秒差距大約是三十光年，
[01:44] 大約就是這顆恆星的距離。
[01:49] 這就是描述恆星亮度的方法。
[01:52] 想一想：為何用對數定義星等？
[01:59] 為甚麼要用對數？
[02:05] 為甚麼用對數來定義恆星亮度？
[02:10] 為何這比直接說通量更方便？
[02:20] 因為你要表示光……
[02:23] 為甚麼比較容易？
[02:26] 光的數值可以很大，對嗎？
[02:29] 對，在這方面會很困難。
[02:31] 對，很好。亮度和距離都有影響。
[02:37] 距離也可以相差極大，從太陽，
[02:43] 直到接近可觀測宇宙的邊緣。
[02:47] 數值可以相差非常大。
[02:50] 所以用對數表示它們更方便。
Logarithmic scales appear well beyond astronomy, including in sound measurements and patterns in numerical data. Benford's law provides a further example of logarithmic reasoning and prompts a discussion of statistical checks on fabricated data.
[00:00] Logarithms are an interesting way to think about the world.
[00:05] We are very used to thinking in linear scales.
[00:09] But nature is often organised on logarithmic scales.
[00:16] Take sound, for example.
[00:19] There is breathing, a jet engine, and fireworks.
[00:25] These are all sounds that our ears can hear.
[00:28] The scale is definitely not linear.
[00:33] Think about the amplitude of the fluctuations.
[00:41] Sound is a density wave propagating through air.
[00:47] Fluctuations in the air allow us to hear sound.
[00:53] The amplitudes can be extremely different.
[00:59] A logarithm gives us a reasonable scale.
[01:03] Otherwise, the amplitudes differ enormously.
[01:07] Many aspects of nature follow logarithmic scales.
[01:13] Another way to see this is through statistics.
[01:19] For example, count the different digits on web pages.
[01:25] Collect a large enough sample, perhaps a million pages.
[01:33] How often do one, two, three, four, and so on appear?
[01:41] You will find what is called Benford's law.
[01:46] The digit one appears much more often;
[01:49] two appears less often, and so on.
[01:53] First, imagine why this would happen.
[02:00] Naively, I collected random web pages,
[02:04] so these numbers should appear randomly.
[02:09] You might expect every digit to have the same probability.
[02:15] The same probability of appearing.
[02:18] But the probability of one is much larger.
[02:24] You can also do statistics on names.
[02:27] For example, my name is Wang Yi.
[02:30] You could look for Wang Er, Wang San, Wang Ba, and so on.
[02:33] They have different probabilities too.
[02:36] But that may not be as general as this.
[02:40] So, why does this happen?
[02:46] Why are the statistics different?
[02:52] After class, you can test it with your coding agent.
[02:58] An assumption that numbers are uniformly distributed
[03:04] depends on the scale on which they are uniform.
[03:09] Real-world numbers are more likely to be roughly uniform
[03:15] on a logarithmic scale than on a linear scale.
[03:19] If numbers are roughly uniform on a logarithmic scale,
[03:26] they satisfy Benford's law.
[03:29] Logarithms are therefore a very helpful way
[03:35] to understand our universe.
[03:41] Things often span multiple orders of magnitude.
[03:47] Logarithmic distributions can arise naturally.
[03:50] This also affects how people fabricate numbers
[03:56] and how fraudulent research papers can be detected.
[04:03] Some people fake numbers. Never do that in research.
[04:08] They fake numbers without knowing Benford's law.
[04:13] The numbers should follow this distribution,
[04:17] but a random number generator gives a different one.
[04:21] If they fake enough numbers for statistics to tell,
[04:26] then one knows that they are fake.
[04:31] That is just a remark about logarithms.
[00:00] 對數是理解世界的一個有趣方式。
[00:05] 我們很習慣用線性尺度思考。
[00:09] 但自然界往往按對數尺度組織。
[00:16] 例如聲音。
[00:19] 有呼吸聲、噴射引擎聲和煙花聲。
[00:25] 這些都是耳朵能聽到的聲音。
[00:28] 這個尺度絕對不是線性的。
[00:33] 想想波動的振幅。
[00:41] 聲音是在空氣中傳播的密度波。
[00:47] 空氣的波動讓我們聽到聲音。
[00:53] 這些振幅可以相差極大。
[00:59] 取對數就能得到合理的尺度。
[01:03] 否則振幅之間會相差極大。
[01:07] 自然界很多現象都呈現對數尺度。
[01:13] 另一種理解方法是做統計。
[01:19] 例如統計網頁上不同數字的出現次數。
[01:25] 收集足夠大的樣本，例如一百萬個網頁。
[01:33] 一、二、三、四等數字各出現多少次？
[01:41] 你會發現所謂的本福特定律。
[01:46] 數字一出現得多很多，
[01:49] 二出現得較少，如此類推。
[01:53] 先想一想，為甚麼會這樣？
[02:00] 直覺上，我隨機收集了網頁，
[02:04] 所以這些數字應該隨機出現。
[02:09] 你可能以為每個數字出現的機會相同。
[02:15] 它們應該有相同的出現機率。
[02:18] 但一出現的機率高得多。
[02:24] 你也可以統計名字。
[02:27] 例如，我叫王一。
[02:30] 你可以找王二、王三、王八等名字。
[02:33] 它們出現的機率也不同。
[02:36] 但這可能沒有這個規律那麼普遍。
[02:40] 那麼，為甚麼會這樣？
[02:46] 為甚麼統計結果會不同？
[02:52] 課後可以用你的編程代理測試一下。
[02:58] 假設數字均勻分佈，
[03:04] 要看它們在哪個尺度上均勻分佈。
[03:09] 現實世界的數值更可能大致均勻地
[03:15] 分佈於對數尺度，而不是線性尺度。
[03:19] 如果數值在對數尺度上大致均勻分佈，
[03:26] 它們就符合本福特定律。
[03:29] 因此，對數很有助於
[03:35] 理解我們的宇宙。
[03:41] 事物的數值往往跨越多個數量級。
[03:47] 對數分佈有時是自然出現的。
[03:50] 這也影響人們怎樣捏造數字，
[03:56] 以及怎樣找出造假的研究論文。
[04:03] 有人捏造數字。做研究千萬不要這樣。
[04:08] 他們捏造數字，卻不知道本福特定律。
[04:13] 這些數字本來應該符合這種分佈，
[04:17] 但隨機數產生器會給出不同的分佈。
[04:21] 如果捏造的數字夠多，統計能分辨，
[04:26] 就知道這些數字是假的。
[04:31] 這只是關於對數的一個補充。
Stellar colours provide clues to temperature through the approximate behaviour of thermal radiation. Spectral classifications and Wien's displacement law connect colour with physical properties, before the discussion returns to the challenge of measuring distance.
[00:00] That was a remark about logarithms.
[00:01] What about colour? What information does it give us?
[00:07] Colour, or light frequency, is what we see through a telescope.
[00:14] What does a star's colour tell us about the star?
[00:26] When discussing the Sun, what did we relate colour to?
[00:31] Temperature. Yes, temperature.
[00:35] Colour is related to temperature in blackbody radiation.
[00:38] This is not a physics class, so I won't explain it in detail.
[00:44] Roughly, when something emits light because it is hot,
[00:49] its colour is related to its temperature.
[00:52] In astronomy, there are different spectral types:
[00:57] O, B, A, F, G, K and M.
[01:01] The different spectral types correspond to different colours.
[01:07] Even I don't remember each one; you needn't memorise them.
[01:11] But when you see this classification, know what it means.
[01:17] Physically, multiply the light's wavelength by temperature.
[01:22] The result is about three times ten to the minus three,
[01:29] in metre-kelvin.
[01:32] This is known as Wien's displacement law.
[01:37] It relates temperature to the wavelength of light.
[01:41] It also means frequency and temperature are proportional.
[01:46] That is also related to the nature of photons.
[01:53] Hotter means bluer; cooler means redder.
[01:58] Remember: hotter is bluer, and cooler is redder.
[02:05] Then, how far away is the star? We already mentioned this.
[02:09] I won't dwell on it: for nearby stars, we use parallax.
[02:15] For more distant stars, I'll discuss other methods later.
[02:22] These methods study stars farther away.
[02:25] Measuring distance is indeed difficult.
[02:28] For now, assume we can learn at least how far away a star is.
[00:00] 這是關於對數的一點補充。
[00:01] 那麼顏色呢？它提供甚麼資訊？
[00:07] 顏色或光的頻率，是望遠鏡直接觀測到的。
[00:14] 恆星的顏色告訴我們甚麼？
[00:26] 談太陽時，我們說顏色與甚麼有關？
[00:31] 溫度。對，就是溫度。
[00:35] 黑體輻射的顏色與溫度有關。
[00:38] 這不是物理課，我不會詳細解釋黑體輻射。
[00:44] 大致來說，當物體因為熱而發光，
[00:49] 它的顏色就與溫度有關。
[00:52] 天文學把光譜分成不同類型：
[00:57] O、B、A、F、G、K 和 M 型。
[01:01] 不同光譜類型對應不同顏色。
[01:07] 我也記不住各型，你們不用背誦。
[01:11] 但看到這種分類時，要知道它在說甚麼。
[01:17] 從物理上說，把光的波長乘以溫度。
[01:22] 結果約為三乘以十的負三次方，
[01:29] 單位是米乘開爾文。
[01:32] 這稱為維恩位移定律。
[01:37] 它描述溫度與光波長的關係。
[01:41] 這也表示頻率與溫度成正比。
[01:46] 這也與光子的本質有關。
[01:53] 越熱越偏藍，越冷越偏紅。
[01:58] 記住：越熱越藍，越冷越紅。
[02:05] 那恆星有多遠？我們已經談過。
[02:09] 不再詳談；附近恆星的距離用視差測量。
[02:15] 更遠的恆星，稍後會介紹其他測量方法。
[02:22] 用這些方法研究較遠的恆星。
[02:25] 測量距離確實很困難。
[02:28] 暫且假設，我們至少能知道恆星有多遠。
Binary stars make stellar masses accessible through orbital motion. Resolved orbits and Doppler measurements provide complementary approaches, while the mass–luminosity relation illustrates how a log–log plot can reveal a power-law relationship.
[00:00] Sometimes we also want to know the mass of a star.
[00:06] How do we determine a star's mass?
[00:11] We usually use solar masses as the unit.
[00:14] For example, a star of ten or 0.3 solar masses.
[00:20] We use this unit because the Sun is a fairly typical star.
[00:25] But when we see a star in the sky, how do we know its mass?
[00:32] It is hard to tell by direct observation.
[00:37] What if we use observations and a little Newtonian mechanics?
[00:44] Can you imagine how we could determine the mass?
[00:56] It is difficult to know every individual star's mass.
[01:00] Fortunately, most stars in the universe are in binary systems.
[01:07] If we see a binary, with two stars orbiting each other,
[01:12] we can measure the stars' masses.
[01:16] Think: how can a binary system give us the star's mass?
[01:28] There are two ways to do this.
[01:33] First, if the telescope has sufficiently good resolution,
[01:40] and the stars are nearby enough to resolve,
[01:46] we can see the two stars individually.
[01:52] We can then calculate the separation between them.
[01:57] Observe their positions at different times,
[02:03] and we can determine their orbital period.
[02:08] With a few steps of Newtonian mechanics,
[02:15] the separation and period give the system's total mass.
[02:20] That is one way to measure the mass.
[02:24] More often, the telescope's resolution is not good enough.
[02:32] Sensitivity may be cheaper to improve than resolution.
[02:38] Resolution is limited by the size of the lens
[02:43] and by fluctuations in the air, among other things.
[02:48] For sensitivity, we improve the sensor as much as we can.
[02:54] That is more under our control.
[02:58] Even if we cannot resolve the stars, we can use their spectra.
[03:04] We can study the binary, not through its orbital radii,
[03:09] because we cannot see the separate stars or their orbits.
[03:14] But we can see velocity changes through the Doppler effect.
[03:20] We infer the velocities of the two stars.
[03:26] Again, using the period—the time for one cycle—
[03:33] and the velocities, we can determine the stars' masses.
[03:37] Not every star's mass is measurable, only favourable cases.
[03:44] But there are so many stars that we have many such cases.
[03:56] So we obtain luminosity from flux and distance.
[04:02] We obtain temperature from colour.
[04:05] And we obtain stellar masses from binary motion.
[04:09] Also, you can imagine a relation between luminosity and mass.
[04:16] For most stars, this relation is fairly simple:
[04:22] a more massive star is brighter.
[04:29] Why? A larger star has higher pressure at its centre.
[04:35] Higher central pressure means more nuclear reactions,
[04:41] making the star brighter.
[04:44] Explaining this slope in detail requires more work.
[04:55] Notice that this figure uses logarithmic scales on both axes.
[05:01] If mass and luminosity follow a power law,
[05:07] they form a straight line on a log–log plot.
[05:15] Measuring the slope helps us extract the power-law relation.
[05:24] In future research, or in other work,
[05:30] if you suspect two variables follow a power law,
[05:37] make a log–log plot and measure its slope.
[00:00] 有時我們也想知道恆星的質量。
[00:06] 如何確定恆星的質量？
[00:11] 通常以太陽質量為單位。
[00:14] 例如十個或零點三個太陽質量的恆星。
[00:20] 用這單位，因為太陽是頗典型的恆星。
[00:25] 但看見天上的恆星，如何知道它的質量？
[00:32] 單靠直接觀測，很難得知。
[00:37] 若結合觀測與一點牛頓力學呢？
[00:44] 你能想像如何確定質量嗎？
[00:56] 很難知道每顆恆星的質量。
[01:00] 幸好，宇宙中大部分恆星都在雙星系統裏。
[01:07] 若看到兩顆恆星互相繞行的雙星，
[01:12] 便可以測量它們的質量。
[01:16] 想一想：如何利用雙星測量質量？
[01:28] 有兩種方法。
[01:33] 首先，如果望遠鏡的解析度夠高，
[01:40] 而恆星又近得足以分辨，
[01:46] 我們便能分別看見兩顆恆星。
[01:52] 然後計算它們之間的距離。
[01:57] 再觀察它們在不同時間的位置，
[02:03] 便能得出公轉週期。
[02:08] 利用幾步牛頓力學的計算，
[02:15] 距離和週期便給出系統的總質量。
[02:20] 這是測量質量的一種方法。
[02:24] 但通常望遠鏡的解析度不夠高。
[02:32] 有時提高靈敏度，比提高解析度便宜。
[02:38] 解析度受透鏡尺寸限制，
[02:43] 也受空氣擾動等因素限制。
[02:48] 至於靈敏度，就盡量改善感測器。
[02:54] 這較容易由我們控制。
[02:58] 即使分不開兩顆恆星，仍能利用光譜。
[03:04] 研究雙星，不是靠軌道半徑，
[03:09] 因為我們分不開恆星，也看不到軌道。
[03:14] 但可透過多普勒效應觀察速度變化。
[03:20] 從而推算兩顆恆星的速度。
[03:26] 再利用週期，也就是完成一圈的時間，
[03:33] 以及速度，便能確定恆星的質量。
[03:37] 並非每顆都能測量，只有條件合適的例子。
[03:44] 但恆星很多，所以合適的例子也很多。
[03:56] 因此，從通量和距離可得光度。
[04:02] 從顏色可得溫度。
[04:05] 從雙星運動可得恆星質量。
[04:09] 另外，可以想像光度與質量有關係。
[04:16] 對大多數恆星，這關係頗簡單：
[04:22] 質量越大的恆星，越明亮。
[04:29] 為甚麼？較大的恆星，中心壓力更高。
[04:35] 中心壓力更高，核反應便更多，
[04:41] 所以恆星更明亮。
[04:44] 但要詳細解釋這斜率，就需要更多分析。
[04:55] 注意，這圖的兩條軸都是對數刻度。
[05:01] 若質量與光度符合冪次定律，
[05:07] 在雙對數圖上便會形成直線。
[05:15] 測量斜率，便可求出冪次關係。
[05:24] 將來做研究或其他工作時，
[05:30] 若懷疑兩個變數符合冪次定律，
[05:37] 便畫雙對數圖，測量它的斜率。
Choosing temperature and luminosity as the axes reveals a powerful way to organise stellar observations: the Hertzsprung–Russell diagram. Its main sequence and other regions show patterns in the stellar population, while comparisons at fixed temperature or luminosity allow stellar sizes to be inferred.
[00:00] We have colour, brightness, mass,
[00:04] distance and location.
[00:06] Location and distance are not intrinsic properties.
[00:10] We have these properties of stars.
[00:14] How do we organise and visualise them?
[00:20] Data visualisation is extremely important
[00:25] for identifying patterns and understanding things.
[00:28] How can we present these variables more intuitively?
[00:34] When we observe millions of stars,
[00:41] can we find some patterns?
[00:45] How do we visualise them?
[00:48] I am not sure whether it is the best way,
[00:54] but two-dimensional plots are very intuitive.
[00:59] How do we choose two of these four variables
[01:03] to put stars on a two-dimensional plot?
[01:08] Each star corresponds to one point on the plot.
[01:12] How should I do it?
[01:15] Data visualisation may look trivial,
[01:21] but it is actually extremely important
[01:25] when we want to understand things intuitively.
[01:31] If you have collected lots of star data, how will you plot it?
[01:38] The first principle is to choose two variables.
[01:50] Just choose two of these four. What would you choose?
[01:57] Temperature and brightness.
[01:59] Oh, colour and brightness.
[02:03] Why do you choose these two: colour and brightness?
[02:08] Yes, very good.
[02:12] Colour and temperature are basically the same thing.
[02:18] Brightness and luminosity too, so we choose these two.
[02:25] We avoid mass and distance. Mass is intrinsic
[02:30] and important, but it is not observed so directly.
[02:34] For many stars, we do not have direct mass information.
[02:40] Distance is not an intrinsic property.
[02:43] So we plot colour, or temperature,
[02:47] against brightness, or luminosity.
[02:49] This is the Hertzsprung–Russell diagram.
[02:54] Simply choosing which parameters to plot
[03:00] can give us a lot of information.
[03:04] Those who made this diagram deserve to be remembered.
[03:10] We call it HR. In a company, HR means human resources.
[03:16] They manage people. Here it is 'star resources'!
[03:22] We manage stars with the HR diagram. Here is a typical one.
[03:28] The horizontal axis shows colour: redder here,
[03:34] and bluer here.
[03:40] As we mentioned, colour corresponds to temperature.
[03:46] Redder means cooler; bluer means hotter.
[03:52] So colour and temperature are basically the same thing.
[03:56] Here we have luminosity and absolute magnitude.
[04:01] How many times brighter is a star than the Sun?
[04:07] For magnitude, more negative means brighter.
[04:12] That is just the convention. This is an HR diagram.
[04:19] What do you observe from this diagram?
[04:25] Very naively, assume every star is the same.
[04:30] That is definitely not true, but suppose they are similar.
[04:35] Then what can you conclude from this diagram?
[04:46] Later, we will see that stars are actually quite different.
[04:50] For now, just ignore those differences.
[05:01] We see most stars in their 'adult' stage,
[05:05] and some at other ages.
[05:08] Most stars lie along this line: the main sequence.
[05:14] These are main-sequence stars.
[05:19] Others lie beyond it. What are those stars?
[05:24] How is a star born, and how does it enter the main sequence?
[05:29] And how does it eventually leave the main sequence?
[05:35] These will be central questions.
[05:37] First, let us understand the HR diagram more intuitively.
[05:42] For example, how can we understand a star's size?
[05:46] Which of these two stars is larger?
[05:55] Or these two: which is larger?
[05:59] How can I understand stellar size from this HR diagram?
[06:11] If they have the same temperature,
[06:14] does a higher magnitude mean larger or smaller?
[06:18] Larger. Yes, intuitively, it is larger. What is the law?
[06:23] By how much? For example, at the same temperature,
[06:28] with twice the brightness, what is the ratio of radii?
[06:40] The square root of two? Yes, very good.
[06:43] We said that, at the same temperature,
[06:49] power per unit area follows the Stefan–Boltzmann law.
[06:54] So it comes down to the star's surface area.
[06:57] Radius is proportional to the square root of area.
[07:01] Surface area is radius squared times four pi.
[07:05] At the same temperature, this is a smaller star,
[07:09] and this is a larger star.
[07:13] Similarly, at the same brightness,
[07:19] this star is smaller, and this one is larger.
[07:24] Because equal brightness means the same temperature.
[07:30] Sorry, let me say that again.
[07:33] The same brightness means the same total power.
[07:37] The same brightness means the same total power.
[07:39] For that total power, the power per area is higher here,
[07:46] and lower here.
[07:49] To give the same total power, the area here must be larger.
[07:54] So we can also infer a star's size from this diagram,
[08:00] using the law we mentioned earlier.
[00:00] 我們有顏色、亮度、質量，
[00:04] 還有距離和位置。
[00:06] 位置和距離不是恆星的內在性質。
[00:10] 我們知道恆星的這些性質。
[00:14] 怎樣整理和呈現這些資料呢？
[00:20] 資料視覺化非常重要，
[00:25] 能幫助我們找出規律、理解事物。
[00:28] 怎樣更直觀地呈現這些變數？
[00:34] 當我們觀測數百萬顆恆星，
[00:41] 能找出一些規律嗎？
[00:45] 怎樣把它們呈現出來？
[00:48] 我不肯定這是不是最好的方法，
[00:54] 但二維圖表至少很直觀。
[00:59] 怎樣從這四個變數中選出兩個，
[01:03] 把恆星放在二維圖上？
[01:08] 每顆恆星對應圖上的一個點。
[01:12] 應該怎樣做呢？
[01:15] 資料視覺化看似很簡單，
[01:21] 但其實非常重要，
[01:25] 尤其當我們想直觀地理解事物。
[01:31] 收集了大量恆星資料，會怎樣畫圖？
[01:38] 第一步是選出兩個變數。
[01:50] 從這四個中選兩個，你會選甚麼？
[01:57] 溫度和亮度。
[01:59] 噢，顏色和亮度。
[02:03] 為甚麼選顏色和亮度這兩個？
[02:08] 對，很好。
[02:12] 顏色和溫度基本上是同一回事。
[02:18] 亮度和光度也是，所以選這兩項。
[02:25] 不選質量和距離。質量是內在性質，
[02:30] 很重要，但不能那麼直接地觀測。
[02:34] 很多恆星都沒有直接的質量資料。
[02:40] 距離也不是恆星的內在性質。
[02:43] 所以我們把顏色，也就是溫度，
[02:47] 與亮度，也就是光度，放在圖上。
[02:49] 這就是赫羅圖。
[02:54] 單是決定把哪些參數放在圖上，
[03:00] 已經能帶來很多資訊。
[03:04] 提出這幅圖的人值得我們記住。
[03:10] 簡稱 HR；公司裏的 HR 是人力資源。
[03:16] 管理人員；這裏則是「恆星資源」！
[03:22] 用赫羅圖管理恆星。這是典型例子。
[03:28] 橫軸表示顏色：這邊比較紅，
[03:34] 這邊比較藍。
[03:40] 正如剛才說的，顏色對應溫度。
[03:46] 越紅，溫度越低；越藍，溫度越高。
[03:52] 所以顏色和溫度基本上是同一回事。
[03:56] 這裏則是光度和絕對星等。
[04:01] 這顆恆星比太陽亮多少倍？
[04:07] 星等越負，表示越亮。
[04:12] 這只是約定。這就是赫羅圖。
[04:19] 從這幅圖，你觀察到甚麼？
[04:25] 很粗略地假設每顆恆星都一樣。
[04:30] 這當然不是真的，但先假設它們相似。
[04:35] 那你能從這幅圖得出甚麼結論？
[04:46] 稍後會看到，恆星其實很不一樣。
[04:50] 現在先忽略這些差別。
[05:01] 我們看到的恆星，大多處於「成年期」，
[05:05] 也有一些處於其他年齡。
[05:08] 大多數恆星沿着這條線排列：主序。
[05:14] 這些就是主序星。
[05:19] 其他恆星在主序之外，它們是甚麼？
[05:24] 恆星怎樣誕生，又怎樣進入主序？
[05:29] 最終又怎樣離開主序？
[05:35] 這些會是我們的核心問題。
[05:37] 先來更直觀地理解赫羅圖。
[05:42] 例如，怎樣判斷恆星的大小？
[05:46] 這兩顆恆星，哪一顆比較大？
[05:55] 或者這兩顆，哪一顆比較大？
[05:59] 怎樣從赫羅圖理解恆星的大小？
[06:11] 如果溫度相同，
[06:14] 較高的星等表示較大，還是較小？
[06:18] 較大。對，直觀上是較大。甚麼定律？
[06:23] 大多少呢？例如，溫度相同，
[06:28] 亮度是兩倍，半徑相差多少？
[06:40] 根號二？對，很好。
[06:43] 剛才說過，在相同溫度下，
[06:49] 每單位面積的功率遵循斯特藩–玻爾茲曼定律。
[06:54] 所以關鍵就是恆星的表面積。
[06:57] 半徑與表面積的平方根成正比。
[07:01] 表面積等於半徑平方乘以四倍圓周率。
[07:05] 在相同溫度下，這顆恆星比較小，
[07:09] 這顆恆星比較大。
[07:13] 同樣，在相同亮度下，
[07:19] 這顆較小，這顆較大。
[07:24] 因為亮度相同，就有相同的溫度。
[07:30] 抱歉，讓我重新說一次。
[07:33] 亮度相同，表示總功率相同。
[07:37] 亮度相同，表示總功率相同。
[07:39] 總功率一樣，這邊每單位面積的功率較大，
[07:46] 這邊則較小。
[07:49] 要有相同總功率，這邊的面積就要較大。
[07:54] 所以也能從這幅圖推斷恆星的大小，
[08:00] 利用剛才提過的定律。
Groups of stars with similar birth times make stellar evolution easier to investigate. Comparing clusters shows stars entering and leaving the main sequence, becoming giants or supergiants, and leaving white-dwarf remnants. The closing review connects these observations with the lecture's opening question about understanding long-lived stars.
[00:00] As I mentioned, a typical star spends most of its time
[00:05] on the main sequence, so we infer
[00:09] that it spends a longer time here.
[00:15] Like the problem of a fly looking at humans,
[00:21] if we want more information, we face a difficulty.
[00:24] This diagram alone cannot tell us much more.
[00:27] But what we can do is look at clusters of stars.
[00:33] We can look at star clusters.
[00:39] First, we use a little physics
[00:44] and carry out some verification.
[00:48] Then we know that stars within a cluster
[00:54] are, roughly speaking, the same age.
[00:58] A region of gas in the galaxy becomes unstable,
[01:03] and stars form at different places within it.
[01:08] So stars in a cluster have roughly the same age,
[01:13] with a common birth time and birthplace.
[01:18] We can use the cluster to understand stars.
[01:25] For example, this is a fairly young star cluster.
[01:31] Its age can be measured independently by other means.
[01:37] For example, how much lithium is in its stars?
[01:43] That can indicate how young those stars are.
[01:45] For the oldest star clusters,
[01:50] we can measure the temperature of their white dwarfs
[01:55] to understand how old they are.
[01:58] So we can independently measure a cluster's age.
[02:03] This one is fairly young.
[02:08] Of course, we cannot follow the same cluster
[02:12] over billions of years.
[02:15] But we can measure different clusters and use statistics.
[02:20] As time passes, we see different features
[02:24] on the H–R diagram. Let's look at them one by one.
[02:29] This is zero, and this is ten million years.
[02:34] What difference do you see between the two?
[02:38] Zero and ten million years: what changes?
[02:42] Sorry? They become cooler?
[02:47] Can we see that they become cooler?
[02:51] It isn't very obvious. Maybe a little.
[02:55] That's a nice observation.
[02:58] Yes, they spend more energy.
[03:01] But that is less obvious than the change on this side.
[03:06] Focus here: this side becomes lower.
[03:12] And some stars come out of the main sequence.
[03:17] What do these changes correspond to?
[03:23] What happens to the stars so that this part lowers
[03:28] and some stars leave the main sequence?
[03:32] First, recall the stars here and here.
[03:37] What is the difference between them?
[03:43] Yes, their radii are different.
[03:48] Are the cooler ones larger or smaller?
[03:52] Larger. So some of these stars become larger.
[03:54] What does that mean?
[04:02] The stars expand, increasing their surface area.
[04:05] These are usually extremely large stars.
[04:08] As I mentioned, luminosity is related to mass.
[04:12] High luminosity here corresponds to high mass.
[04:15] When high-mass stars expand,
[04:20] they become what we call red supergiants.
[04:25] Lower-mass stars eventually become red giants.
[04:27] So some stars, at a later stage,
[04:32] leave the main sequence.
[04:35] They move from middle age into old age.
[04:40] Later, we'll discuss the physics of why they leave.
[04:43] But observation already tells us something.
[04:48] These stars were not on the main sequence: too young.
[04:53] As time passes, they are more likely to join it.
[04:57] This becomes clearer, for example,
[05:01] from ten million to one hundred million years.
[05:06] Most young stars reach the main sequence,
[05:10] while more stars leave it.
[05:13] This is one billion years.
[05:16] More and more stars leave the main sequence.
[05:19] At five billion years, even more have left.
[05:22] And this is ten billion years.
[05:24] From five to ten billion years, what changes?
[05:27] One thing is that more stars leave the main sequence
[05:33] because they are old enough.
[05:37] Apart from that, what difference do you see?
[05:47] You see something here. What are they?
[05:53] There were already some here, but now there are more.
[05:57] And there are things here. What are they?
[06:07] First, this one.
[06:09] If a star lies here, what is it like?
[06:18] Look: it is quite hot, but its luminosity is low.
[06:23] It is smaller. Yes, these stars are very small.
[06:27] That usually means a much higher density,
[06:30] if the star hasn't lost too much mass.
[06:34] Much denser, much smaller, but still hot.
[06:37] What kind of star could it be?
[06:44] They are white dwarfs.
[06:47] White dwarfs appear as remnants of dead stars.
[06:53] And what is this one?
[06:57] It's a little harder to imagine: a different type of star.
[07:02] This one is burning hydrogen,
[07:07] while this one is burning helium.
[07:09] It follows different rules, so it becomes different.
[07:14] The lesson we learn from this is that
[07:20] just from observation and elementary physical laws,
[07:25] we can understand a lot about a star's lifetime.
[07:30] That was our promise at the start of the lecture:
[07:33] a fly can observe humans and learn a lot about them.
[07:38] That is what we'd like to say in today's lecture.
[07:43] We began with the Nobel Prize and neutrinos.
[07:47] Then, in the main part, we started with
[07:51] a fly looking at humans.
[07:54] We considered the main observations from a telescope.
[07:59] From those observations, we can extract
[08:03] a star's mass and brightness,
[08:07] its distance and its colour.
[08:11] We choose the stars' colour
[08:16] and luminosity to plot an H–R diagram.
[08:20] From the H–R diagram, just through observation
[08:24] and a little physics, we learn a lot about stars.
[08:31] That's today's lecture. I invite you to think ahead
[08:35] to our next lecture on the physics of stars.
[08:39] Don't be afraid of the physics:
[08:44] it is elementary, even common-sense physics.
[08:47] What more can physics tell us about the stars?
[08:52] That's it for today.
[00:00] 正如剛才所說，恆星大部分時間
[00:05] 都在主序上，所以我們推斷
[00:09] 它在這裏停留的時間較長。
[00:15] 就像蒼蠅觀察人類的問題，
[00:21] 想取得更多資料，就遇到困難。
[00:24] 單靠這幅圖，很難知道更多。
[00:27] 但我們可以觀察星團。
[00:33] 我們可以研究成群的恆星。
[00:39] 首先，我們用一點物理知識，
[00:44] 再作一些驗證。
[00:48] 於是知道，一個星團內的恆星
[00:54] 大致上都是同齡的。
[00:58] 星系內的一片氣體變得不穩定，
[01:03] 並在其中不同位置形成恆星。
[01:08] 所以星團內的恆星大致同齡，
[01:13] 有共同的誕生時間和地點。
[01:18] 我們可利用星團理解恆星的性質。
[01:25] 例如，這是一個相當年輕的星團。
[01:31] 其年齡可用其他方法獨立測量。
[01:37] 例如，當中的恆星含有多少鋰？
[01:43] 這可反映那些年輕恆星的年齡。
[01:45] 至於最古老的星團，
[01:50] 我們可測量其中白矮星的溫度，
[01:55] 了解它們的年齡。
[01:58] 因此，星團年齡可獨立測量。
[02:03] 這一個星團相當年輕。
[02:08] 當然，我們不能一直觀察同一星團，
[02:12] 等待數十億年。
[02:15] 但可測量不同星團，作統計分析。
[02:20] 隨着時間推移，我們看見不同特徵，
[02:24] 在赫羅圖上逐一看看。
[02:29] 這是零歲，這是一千萬年。
[02:34] 兩者之間有甚麼分別？
[02:38] 零歲和一千萬年，有甚麼變化？
[02:42] 甚麼？它們變冷了？
[02:47] 我們看得出它們變冷嗎？
[02:51] 不太明顯，也許有一點。
[02:55] 這是個很好的觀察。
[02:58] 對，它們消耗更多能量。
[03:01] 但這不及這一邊的變化明顯。
[03:06] 先看這裏，這一邊降低了。
[03:12] 而有些恆星離開了主序。
[03:17] 這些變化代表甚麼？
[03:23] 恆星發生了甚麼，令這部分降低，
[03:28] 並使一些恆星離開主序？
[03:32] 先回想一下，這裏和那裏的恆星。
[03:37] 它們之間有甚麼分別？
[03:43] 對，它們的半徑不同。
[03:48] 較冷的恆星是更大，還是更小？
[03:52] 更大。所以這裏有些恆星變大。
[03:54] 這代表甚麼？
[04:02] 恆星膨脹，表面積增加。
[04:05] 這些通常是非常大的恆星。
[04:08] 如剛才所說，光度與質量有關。
[04:12] 這裏的高光度對應高質量。
[04:15] 當高質量恆星膨脹時，
[04:20] 它們成為所謂的紅超巨星。
[04:25] 較低質量的恆星則成為紅巨星。
[04:27] 所以，有些恆星到了較後的階段，
[04:32] 便離開主序。
[04:35] 它們由中年步入老年。
[04:40] 稍後再談它們離開主序的物理原因。
[04:43] 但單靠觀察，我們已知道一些事。
[04:48] 這些星原本太年輕，還未在主序上。
[04:53] 隨着時間推移，它們更可能進入主序。
[04:57] 例如，這種變化會更加明顯，
[05:01] 由一千萬年到一億年的時候。
[05:06] 大部分年輕恆星進入主序，
[05:10] 同時有更多恆星離開主序。
[05:13] 這裏是十億年。
[05:16] 越來越多恆星離開主序。
[05:19] 到五十億年，離開的恆星更多。
[05:22] 這裏是百億年。
[05:24] 從五十億到百億年，有甚麼變化？
[05:27] 首先，有更多恆星離開主序，
[05:33] 因為它們已達到相應的年齡。
[05:37] 除此之外，還看到甚麼分別？
[05:47] 這裏出現了一些東西，是甚麼？
[05:53] 這裏原本已有一些，現在更多了。
[05:57] 這裏也有一些，是甚麼呢？
[06:07] 先看這一個。
[06:09] 若一顆恆星在這裏，它有甚麼性質？
[06:18] 看，它很熱，但光度很低。
[06:23] 它更小。對，這些恆星非常小。
[06:27] 這通常代表密度高得多，
[06:30] 前提是恆星沒有失去太多質量。
[06:34] 密度更高、體積更小，但仍然很熱。
[06:37] 這會是哪一種恆星？
[06:44] 它們是白矮星。
[06:47] 白矮星是死亡恆星留下的殘骸。
[06:53] 那這一個是甚麼？
[06:57] 這較難想像，是另一類恆星。
[07:02] 這一類在燃燒氫，
[07:07] 而這一類在燃燒氦。
[07:09] 它遵循不同規則，所以性質不同。
[07:14] 我們從中學到的是，
[07:20] 單靠觀察和最基本的物理定律，
[07:25] 已可理解很多恆星一生的事情。
[07:30] 這就是課堂開始時提出的目標：
[07:33] 蒼蠅觀察人類，也可了解很多事情。
[07:38] 這就是今天這堂課想說明的事。
[07:43] 一開始，我們談諾貝爾獎和中微子。
[07:47] 接着在主要部分，我們先想像
[07:51] 一隻蒼蠅觀察人類。
[07:54] 然後看望遠鏡能取得甚麼觀測資料。
[07:59] 從這些觀測資料，我們可得出
[08:03] 恆星的質量和亮度，
[08:07] 以及它的距離和顏色。
[08:11] 我們選取恆星的顏色，
[08:16] 以及光度，繪製赫羅圖。
[08:20] 利用赫羅圖，單靠觀察，
[08:24] 加上一點物理，已可了解很多星體性質。
[08:31] 今天到此為止。請大家想想下一課，
[08:35] 我們將談恆星的物理。
[08:39] 不用害怕物理，
[08:44] 只是很基本，甚至常識層面的物理。
[08:47] 物理還能讓我們理解恆星的甚麼？
[08:52] 今天就到這裏。