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--- courses:ast100:3 [2024/11/22 07:08] – asad
+++ courses:ast100:3 [2024/11/22 07:44] (current) – [5.3 Black Hole] asad
@@ Line 5: / Line 5: @@
 **Mars:** Peace will come after war. But for now, there’s no way without war. Look ahead — the massive Yarlung Tsangpo Gorge, the deepest and longest canyon on Earth. Its deafening roar will make it impossible for any of us to hear one another.
-**Hermes:** We can hear you clearly. Like the final scene in *Crouching Tiger, Hidden Dragon*, let’s leap from the summit of Namcha Barwa to the very bottom of the gorge. There, amidst all the sounds, we’ll let our words float.
+**Hermes:** We can hear you clearly. Like the final scene in //Crouching Tiger, Hidden Dragon//, let’s leap from the summit of Namcha Barwa to the very bottom of the gorge. There, amidst all the sounds, we’ll let our words float.
 //[Everyone leaps from the mountain summit and, in a moment, lands 7 km below on the banks of the Siang River.]//
@@ Line 69: / Line 69: @@
 **Socrates:** What do you mean by fuel?
-===== - Star Formation =====
+===== - Birth of Stars =====
 {{:bn:courses:ast100:star-formation.webp?nolink|}}
@@ Line 77: / Line 77: @@
 **Juno:** At first, it was just a shapeless cloud, but now I see a red sphere in the center surrounded by a flat disk about half a light-year in size. How did the shapeless cloud transform into a spherical core and flat disk over these few million years?
-**Mars:** To understand that, you need to grasp the difference between **gravity** and **rotation**. If I jump into the swift current of the Aungsui River from this rock, I will survive unscathed. However, I would die if I didn’t land in the water because gravity pulls me toward the Earth's center. The closer an astronaut gets to Earth, the stronger Earth's gravity pulls them. This means gravity always attracts, and the closer you are to the center of gravity, the stronger the pull.
+**Mars:** To understand that, you need to grasp the difference between **gravity** and **rotation**. If I jump into the swift current of the Siang River from this rock, I will survive unscathed. However, I would die if I was alive because gravity pulls me toward the Earth's center. The closer an astronaut gets to Earth, the stronger Earth's gravity pulls them. This means gravity always attracts, and the closer you are to the center of gravity, the stronger the pull.
 **Juno:** Is that why you tied a rock to the end of a rope to explain rotation?
@@ Line 185: / Line 185: @@
 ===== - Death of Stars =====
-**Mars:** The remnants of a star’s death are no less fascinating than its life. To understand white dwarfs, let’s travel back to **1604** and meet Kepler in Prague. That year, Kepler observed a supernova, now known as **Kepler’s Supernova**, whose remnants are about 20,000 light-years away from us. The Chandra X-ray Observatory has captured images showing that, even after 400 years, the explosion’s gas is expanding outward at about 30 million km/h. However, this isn’t like the supernovae I’ve mentioned before. This one didn’t form from a massive star but from a smaller one.
+**Mars:** The remains of a star are no less fascinating than its life. To understand white dwarfs, we need to go back to **1604** and meet Kepler in Prague. That year, Kepler observed a supernova, now known as **Kepler’s Supernova**, whose remnants are about 20,000 light-years away from us. The Chandra X-ray Observatory captured images showing that even 400 years after the explosion, the gas is still expanding outward at a speed of about 30 million kilometers per hour. However, this isn’t the same kind of supernova I mentioned earlier. This one wasn’t formed from a massive star but from a smaller one.
-**Socrates:** Smaller stars form white dwarfs, not supernovae, right?
+**Socrates:** Didn’t you say smaller stars only form white dwarfs, not supernovae?
-**Hermes:** Patience! First, let’s visit Prague in 1604.
+**Hermes:** Patience! First, let’s travel to Prague in 1604.
-//[With Hermes’ help, everyone travels to Prague in 1604, where they find Kepler in a marketplace debating with three others.]//
+//[With Hermes' help, everyone travels to a night in 1604 Prague and finds Kepler in a marketplace, engaged in a mild debate with three others.]//
-**Mars:** Stay invisible, all of you. Let me talk to Kepler.
+**Mars:** Stay invisible, everyone. Let me talk to Kepler.
-**Kepler:** I won’t believe it until I see it with my own eyes—a new star in the sky. I want to believe, though, because it would be another major blow to Aristotle’s theory.
+//[Mars approaches the group Kepler was debating with, while the others remain invisible, observing and listening.]//
+**Kepler:** I won’t believe it until I see it with my own eyes—a new star in the sky. I want to believe, though, because it would deliver another significant blow to Aristotle’s theories.
 **Mars:** I saw it myself just last night.
@@ Line 203: / Line 205: @@
 **Mars:** Look in that direction. It’s still visible. Check your charts to see if that star was supposed to be there.
-**Kepler:** Incredible. It truly is a new star. It wasn’t supposed to be there. Since last night, it’s been visible. Aristotle claimed that nothing new happens in the heavens. He’s been proven wrong. My next task is to complete the burial of Aristotle’s theories by proving Copernicus’ heliocentric model.
+**Kepler:** Incredible. It truly is a new star. It wasn’t supposed to be there. It’s been visible since last night. Aristotle said that nothing new happens in the heavens. He’s been proven wrong. My job now is to properly bury Aristotle’s theories by proving Copernicus’ heliocentric model.
-**Mars:** Did you know that this “new” star is itself a kind of burial?
+**Mars:** Did you know that this new star is also a kind of burial?
 **Kepler:** What do you mean? Who are you? A philosopher?
-**Mars:** You don’t need to know who I am. First, tell me, if I, like Plato’s Timaeus, tell you a plausible story about this “new” star, will you listen?
+**Mars:** Who I am doesn’t matter. First, tell me—if, like Plato’s //Timaeus//, I tell you a plausible story about this "new" star, will you listen?
-**Kepler:** I’m thinking of writing a story myself, called *Somnium*. I’m not averse to stories.
+**Kepler:** I’m considering writing a story myself, called //Somnium//. I’m not averse to stories.
+==== - White Dwarf ====
-==== - White Dwarfs ====
 {{:bn:courses:ast100:white-dwarf.webp?nolink&650|}}
-**Mars:** Then listen. This so-called “new star” was actually part of a **binary system**, meaning it had a companion star. Let’s call the new star **B** and its companion **C**. For about **10 billion years**, B and C orbited each other. However, since B was slightly larger and heavier than C, it died a million years ago, leaving behind a white dwarf—a small but extremely hot remnant that appears white. After a million years of orbiting around B’s corpse, it was C’s turn to die. C swelled up into a **red giant**, becoming enormous but cooler, appearing red. Its size grew so much that B (the white dwarf) started pulling gas from C’s outer layers. This process increased B’s mass until it exceeded **1.4 times the Sun’s mass** yesterday, causing B to collapse inward. However, B’s core was so dense that the gas couldn’t reach the center and bounced off, exploding outward in a massive supernova. That’s why we see B now. It isn’t a new star but the explosion of an old star’s corpse.
+**Mars:** Listen, then. This so-called “new star” was actually part of a **binary system**, meaning it had a companion star. Let’s call the new star **B** and its companion **C**. For about **10 billion years**, B and C orbited each other. However, since B was slightly larger and heavier than C, it died a million years ago, leaving behind a **white dwarf**—a very small but extremely hot remnant that appears white. After orbiting B’s corpse for a million years, C also neared the end of its life, swelling into a **red giant**, becoming enormous but cooler, thus appearing red. C grew so large that B (the white dwarf) began pulling gas from C’s outer layers. As a result, B’s mass gradually increased until, yesterday, it exceeded **1.4 times the Sun’s mass**. This caused B to collapse inward. However, since B’s core was extremely dense, the infalling gas couldn’t reach the center, bouncing off the solid core and exploding outward in a massive supernova. That’s why B is visible now. B isn’t a “new” star—it’s the fresh explosion of an old star’s corpse.
-**Kepler:** Perhaps C was trying to revive B.
+**Kepler:** Perhaps companion C was trying to revive B.
-**Mars:** And it backfired. That’s why I say never try to revive the dead. If Orpheus couldn’t bring back Eurydice, how could C revive B? In reality, the explosion of B sent C flying out of their mutual orbit. C is now a **runaway star**, a solitary wanderer. They’ll never be gravitationally bound again.
+**Mars:** And it backfired. That’s why I always say: never attempt to revive the dead. If Orpheus couldn’t bring back Eurydice, how could C revive B? In reality, B’s massive explosion permanently flung C out of their mutual orbit. C is now a **runaway star**, a solitary wanderer. They’ll never again be gravitationally bound to each other.
-**Kepler:** The dead can’t be revived? That’s not true. Plato revived Socrates. As much as I dislike Tycho Brahe, I must dig up the meaning of his observations, even if it means unearthing his legacy.
+**Kepler:** It’s not true that the dead can’t be revived. Plato revived Socrates. As much as I dislike Tycho Brahe, I must unearth the meaning of his observations, even if it means digging up his legacy.
-//[Kepler turns back to find Mars gone, disappearing in an instant. Hermes takes everyone back to the Siang and Brahmaputra rivers in India.]//
+//[Kepler turns back to find Mars gone, vanishing in an instant. Hermes takes everyone back to the confluence of the Siang and Brahmaputra rivers in India.]//
-==== - Neutron Stars =====
+**Socrates:** Was that really the right thing to do? Poor Kepler—if he can’t calculate Mars’ orbit now, it’ll be all your fault.
-**Mars:** If a star’s core mass is **less than 1.4 times the Sun’s mass**, it becomes a white dwarf. If it’s **more than 1.4 times**, it becomes a neutron star. For a core to reach this critical mass, the star’s initial mass must be at least **8 times the Sun’s mass**. That’s why only stars at least 8 times heavier than the Sun can leave behind a neutron star.
+**Mars:** Do you think I’d let Kepler catch me that easily?
-**Socrates:** You’ve mentioned this **1.4 times** limit before. Why is the limit precisely 1.4 times the Sun’s mass?
+**Socrates:** Well, we’ve now understood white dwarf supernovae quite thoroughly, thanks to this story-like explanation. Now, tell us—what is this white dwarf made of?
-**Mars:** Subrahmanyan Chandrasekhar discovered this famous limit in 1930 while traveling on a ship from Mumbai to Venice. Let me explain without math. Stars are primarily made of **hydrogen (74%)** and **helium (24%)**. Inside stars, the temperature is so high that all atoms lose their electrons, forming a **plasma** of free ions and electrons. After passing through the red giant phase, the core becomes so dense that electrons fight back against gravity by creating **degeneracy pressure**, stabilizing the star as a white dwarf. Chandrasekhar calculated that if the core’s mass exceeds **1.4 times the Sun’s mass**, gravity becomes so strong that electron degeneracy pressure fails. The core then collapses further, breaking apart nuclei, converting protons into neutrons, and forming a neutron star.
+**Mars:** A white dwarf is the highly compressed core of a star, so its density is incredibly high. So high, in fact, that the electrons within it can no longer maintain their usual positions and speeds. Under immense pressure, they are forced much closer together, and their speeds increase far beyond normal. These are known as **degenerate electrons**. Because they resist being forced closer, they collectively create an outward pressure called **degeneracy pressure**. This pressure counteracts gravity, allowing a white dwarf to remain stable for billions of years.
-**Socrates:** And how small are neutron stars?
+**Socrates:** Fascinating. Now, let’s hear about the other two stellar remnants.
+==== - Neutron Stars ====
+**Mars:** If the core mass of a star is less than 1.4 times the Sun’s mass, it becomes a white dwarf upon death. However, if it exceeds 1.4 times, it becomes a neutron star. For a core to reach this critical mass during a star's death, the star’s total mass must be at least 8 times the Sun’s mass. This is why only stars at least 8 times heavier than the Sun can leave behind a neutron star as their remnant.
-**Mars:** Very small. If you compress a Sun-sized star (diameter ~1 million km) to the size of Earth (~10,000 km), you get a white dwarf. If you compress it further to the size of Dhaka city (~10 km), you get a neutron star. With no reduction in mass, the **density increases immensely**: for the Sun, it is approximately 1 g/cm³; for a white dwarf, it reaches around 1 million g/cm³; and for a neutron star, it skyrockets to about 1 trillion g/cm³.
+**Socrates:** You’ve mentioned this “1.4 times” limit before. Why is it precisely 1.4 times the Sun’s mass?
-A **teaspoon** of neutron star material would weigh about **1 trillion kilograms**.
+**Mars:** Subrahmanyan Chandrasekhar (after whom the **Chandra X-ray Observatory** is named) discovered this famous limit in 1930 while traveling on a ship from Mumbai to Venice. Let me explain the **Chandrasekhar Limit** in simple terms, without math. Stars are primarily made of **hydrogen (74%)** and **helium (24%)**. Inside stars, the temperature is so high that electrons are stripped from atoms, leaving ions and free electrons. This creates a plasma—a gas of free protons (from hydrogen nuclei) and electrons. After passing through the red giant phase, the core of the star becomes small and dense. The electrons resist further compression by generating **electron degeneracy pressure**, stabilizing the star as a white dwarf. However, Chandrasekhar calculated that if the core’s mass exceeds **1.4 times the Sun’s mass**, gravity becomes so strong that electron degeneracy pressure can no longer counteract it. The core continues to collapse, breaking apart atomic nuclei, and converting protons into neutrons. These neutrons are packed extremely closely, and their motion generates a new type of pressure called **neutron degeneracy pressure**, which halts further collapse. Stars stabilized by neutron degeneracy pressure are called neutron stars.
-==== - Black Holes ====
+**Socrates:** How small is a neutron star? It must be incredibly compact.
-{{:bn:courses:ast100:black-hole-anatomy.webp?nolink|}}
-**Mars:** If a star’s initial mass is **more than 20 times the Sun’s**, its core’s final mass exceeds **3 solar masses**, and even neutron degeneracy pressure cannot counter gravity. The core collapses into a near-zero point of infinite density, forming a **black hole**.
+**Mars:** Yes. If you compress a Sun-sized star (diameter ~1 million km) to the size of Earth (~10,000 km), you get a white dwarf. Compress it further to the size of Dhaka city (~10 km), and you get a neutron star. With no reduction in mass, the density increases drastically: inside the Sun, it is approximately 1 g/cm³; inside a white dwarf, it reaches around 1 million g/cm³; and inside a neutron star, it skyrockets to about 1 trillion g/cm³.
-**Socrates:** But black holes have size, don’t they?
+This means a **teaspoon** of neutron star material would weigh about **1 trillion kilograms**.
-**Mars:** Yes. This image shows the structure surrounding a black hole. Inside, even light cannot escape due to the immense gravitational pull.
+**Socrates:** And you said earlier that neutron stars are the roundest objects in the universe. Why? The Sun is also round.
-**Socrates:** Is it because of gravity that even light can’t escape?
+**Mars:** The Sun and the Earth are both round, but how round are they? Due to rotation, no object can be perfectly spherical. The Earth, which rotates once every 24 hours, is slightly flattened at the poles. The difference between Earth’s equatorial and polar diameters is **0.3%**, while for the Sun, it’s only **0.0009%**, making the Sun **99.999% perfectly spherical**. Neutron stars are just as spherical as the Sun.
+**Socrates:** But it seems to me that neutron stars should be even more spherical than the Sun. Their higher density means stronger self-gravity, right?
+Here’s the response without bullet points:
+**Mars:** You’re absolutely correct, Socrates. The gravity on a neutron star is immensely strong. Let me explain using weight as an analogy. A person weighing 100 kg on Earth would weigh 1,000 Newtons on Earth’s surface, 30,000 Newtons on the Sun’s surface, and 1 trillion Newtons on a neutron star’s surface. Despite this immense gravity, neutron stars remain as spherical as the Sun because they also spin very rapidly. Some neutron stars rotate up to 1,000 times per second. When a neutron star has a companion star or nearby gas, it can form an accretion disk, similar to protostars or active galaxies. As matter spirals into the neutron star, some of it is ejected along the poles as jets. These jets give rise to a type of neutron star called a **pulsar**.
+Despite this immense gravity, neutron stars remain as spherical as the Sun because they also spin very rapidly. Some neutron stars rotate up to **1,000 times per second**. When a neutron star has a companion star or nearby gas, it can form an **accretion disk**, similar to protostars or active galaxies. As matter spirals into the neutron star, some of it is ejected along the poles as jets. These jets give rise to a type of neutron star called a **pulsar**.
+**Socrates:** Does it have any connection to the word “pulse”?
+{{https://upload.wikimedia.org/wikipedia/commons/4/4d/Lightsmall-optimised.gif?nolink&500}}
+**Mars:** Yes, exactly like this image. The jet of a pulsar emits through a narrow beam, and we can only detect it when the beam is pointed directly at us. Each time the beam sweeps past Earth, telescopes detect a burst of high-energy radiation, creating a “pulse.” For pulsars that rotate 1,000 times per second, we detect 1,000 pulses per second. The first pulsar was discovered in **1967** by Jocelyn Bell Burnell at Cambridge University. Its regular pulses were so precise that some initially mistook them for signals from an alien civilization.
+**Socrates:** Humanity might never fully understand if aliens actually exist. But for now, tell me about black holes. How much larger and denser does a star’s core need to be to form a black hole?
+==== - Black Hole ====
+**Mars:** By now, you understand how a black hole forms. The fundamental challenge of a star’s life is resisting the relentless inward pull of gravity. The Sun does this through **nuclear pressure** and the pressure of hot gases, white dwarfs resist through **electron degeneracy pressure**, and neutron stars through **neutron degeneracy pressure**. However, if a star’s initial mass is **20 times or more** that of the Sun, its core will have a mass of at least **three times** the Sun’s mass at the time of its death. In such cases, even the degeneracy pressure of neutrons cannot counteract gravity. As the outer layers of the core collapse and bounce off the dense inner core, they cause a powerful supernova explosion, called a **hypernova**. After this explosion, the innermost core collapses under gravity into a near-point of infinite density—a **singularity**.
+**Socrates:** But a black hole isn’t just a point. It has size, doesn’t it?
+{{:bn:courses:ast100:black-hole-anatomy.webp?nolink|}}
-**Mars:** Exactly. The escape velocity increases with surface gravity: Earth – 11 km/s, Sun – 600 km/s, White Dwarf – 5,000 km/s, Neutron Star – 100,000 km/s.
+**Mars:** Yes, it does. This image shows the structure surrounding a black hole, or at least its surroundings. The interior can’t be depicted, as nothing, not even light, can escape from within.
-For black holes, the escape velocity exceeds **300,000 km/s**, the speed of light. Thus, even light cannot escape, giving rise to the term **black hole**. The boundary where escape becomes impossible is called the **event horizon**. Inside the event horizon, everything falls toward the singularity, where matter and energy compress infinitely. Outside the event horizon, matter falling in forms an **accretion disk**, ejecting jets along the poles, similar to protostars and pulsars.
+**Socrates:** Is it gravity that prevents light from escaping?
-**Socrates:** So, countless black holes combine to form the **supermassive black holes** we saw during the Galactic Age. But we mustn’t lose ourselves in singularities. The Brahmaputra is calling, and we must return to Earth, five billion years in the past.
+**Mars:** Exactly. The stronger the surface gravity, the harder it is to escape. To escape Earth’s gravity, an object must travel at **11 km/s**. For the Sun, the escape velocity is **600 km/s**; for a white dwarf, it’s **5,000 km/s**; and for a neutron star, it’s about **100,000 km/s**. Since light travels at **300,000 km/s**, even it struggles to escape from a neutron star, getting stretched and redshifted by gravity. A black hole is an object where the escape velocity exceeds the speed of light. Since even light cannot escape, we call it a black hole. While all the energy and matter are concentrated in the **singularity**, the black hole’s gravitational influence extends up to the **event horizon**. Beyond this boundary, nothing can escape—not even light. If something crosses the event horizon, there’s no return. Even approaching the **innermost stable orbit** is dangerous—anything moving closer is destined to cross the event horizon. Just outside this, light bends so much due to gravity that it orbits the black hole like a satellite, forming a spherical **photon sphere**. Like protostars and pulsars, gas falling into a black hole forms a flat **accretion disk** around it. Some of this material is lost forever, but due to the black hole’s rotation, some of it is ejected in jets along the poles at nearly the speed of light.
+**Socrates:** So, what we saw during the Galactic Age as **supermassive black holes** are essentially combination of many such black holes. But let’s not get lost in the singularity. The Brahmaputra is calling. We must now journey back to Earth, five billion years ago.