UNIVERSITY OF COLORADO - COLORADO SPRINGS Black Holes Lab Background Information n 1916 Karl Schwarzschild read Einstein’s paper on general relativity. He was interested in the physics of stars and had a lot of spare time between battles on the Russian front, so he solved I Einstein’s field equation for the region outside a massive spherical object. Although his solution predicted the existence of Black Holes it was disregarded as a mathematical anomaly. There could not actually be any object that is infinitely dense and would warp space-time to such an extreme degree that even light could not escape! Figure 1: "Gargantua", a fictional black hole from the movie “Interstellar”. P E S 1 1 0 0 - GENERAL ASTRONOMY LAB I I Black Hole Formation The lifecycle of a star is determined at its birth. If the star is on the smaller size (less than ~8 times the mass of our Sun) it will end its life as a white dwarf. However, if the amount of material is larger the star will have a very different life and end in a massive supernova explosion and the birth of an object known as a Black Hole. Figure 2: Formation of Black Holes and other interstellar objects. How does one see a black hole if it is so small and invisible? Anything in orbit around a black hole will be subject to large gravitational forces and will be accelerated to incredible velocities that will cause it to heat up to millions of degrees and glow brightly. So bright that this glow can be detected by telescopes. Other black holes have been found by their sheer size and gravitational influence. At the heart of our galaxy, Sagittarius A is thought to be a supermassive black hole that helps keep the galaxy rotating. Almost every galaxy is now thought to house a supermassive black hole at its center, they might even be essential to the formation of a stable galaxy. One of the largest black holes ever recorded was photographed in late 2019. It is the first photograph of its kind (see the figure to the right). Figure 3: First picture of a Black Hole, at the heart of galaxy Messier 87. Black Holes - 2 P E S 1 1 0 0 - GENERAL ASTRONOMY LAB I I Escape velocity Most people think of a black hole as a voracious whirlpool in space, sucking down everything around it. But that is just not the case! A black hole is a place where gravity has gotten so strong that the escape velocity is faster than light. But what does that mean, exactly? Gravity is what keeps us on the Earth, but it can be counteracted. If you throw a rock in the air, it will go up a short height before the Earth’s gravity slows it and pulls it back to the ground. If you throw it a little harder, it goes faster and higher before coming back down. If you could throw the rock hard enough, it would have enough velocity that the Earth’s gravity could not slow it down enough to stop it. The rock would have enough velocity to escape the Earth. On earth in order to counteract the pull of gravity we need to achieve a velocity of 11.2 km/s (25,000 mph)! But an object’s escape velocity depends on its gravity and the gravity an object exerts depends on its mass. The Sun has far more gravity than the Earth, so its escape velocity is much higher—more than 600 km/s. Is it possible for an object to gain enough gravity such that the escape velocity would be higher than the speed of light? Body Mass Escape Velocity The Moon 73,600,000,000,000,000,000 kg 2.38 km/sec 5,323 mph Earth 5,980,000,000,000,000,000,000 kg 11.2 km/sec 25,054 mph Jupiter 715,000,000,000,000,000,000,000,000 kg 59.5 km/sec 133,098 mph Sun 1,990,000,000,000,000,000,000,000,000 kg 618 km/sec 1,382,426 mph Sirius B 2,000,000,000,000,000,000,000,000,000 kg 5,200 km/sec 11,632,069 mph Neutron Star 2,800,000,000,000,000,000,000,000,000 kg 125,000 km/sec 279,600,000 mph Table 1: Velocities needed to break free of the gravitational pull of different objects. Another important aspect of escape velocity is the distance from the center you are trying to “escape”. Examine the case of the Sun and Sirius B (a white dwarf star), both have about the same mass, but the escape velocities are wildly different. Sirius B compacts the mass of the Sun into a package of the size of the Earth. Can you imagine how strong the surface gravity must be Figure 4: Side-by-side comparison between the on Sirius B? Meaning the surface gravity would be Earth and Sirius B. Wikipedia. about 350,000 times greater than on Earth. As seen above we can affect the escape velocity by either increasing the mass or decreasing the size or both. From Einstein we learned that gravity is a result of the distortion of space-time. The more massive the object the greater it affects the warping of space-time. Black Holes - 3 P E S 1 1 0 0 - GENERAL ASTRONOMY LAB I I Figure 5: Bending of space-time by objects of various masses. The whole idea behind a black hole is that the gravity has become so large that it can even overcome atomic or nuclear particle pressure and crush them, allowing the black hole to Within all stars there is a struggle between the gravity due to the mass of the star trying to pull everything to the center and the counter acting force of the pressure due to the heat of star’s internal reactions. Depending, mainly on the initial mass of the star, the balance of these two forces will result in various ends. Star Death state Final Solution to collapse All atoms are stripped of electrons. Free electron cloud pressure 8 – 10.5 M White Dwarf ☉ prevents further gravitational collapse. All atoms destroyed. Only neutrons are left. Neutron degeneracy 10 – 25 M Neutron star ☉ pressure stops gravitational collapse. Subatomic pressures can no longer prevent gravitational collapse. 25+ M Black hole ☉ All mass compressed into an infinity small point, the Singularity. Table 2: Initial mass of a star will determine how the stars life will end. (Unit definition - M☉=”Solar Mass”, Ex: 10 Solar Masses would be a mass equal to 10 of our Suns = 10 M☉) As we saw earlier the escape velocity is dependent on the mass of the object and size of the surface. As seen in the table above despite the tremendous mass contained within a small space a white dwarf or even the neutron star does not have high enough escape velocity to trap the light emitted by these stars. The major deference is that the surface of a black hole is shrunk to an infinity small size. Therefore, the escape velocity from the black hole is greater than the speed of light, 300,000 km/s (670,616,629 mph), and nothing can reach the outside world. It is like a bottomless pit - a black hole. It has been theorized that the “inside” of a black hole is extremely bright illuminated by all the trapped light rays. Black Holes - 4 P E S 1 1 0 0 - GENERAL ASTRONOMY LAB I I Schwarzschild Radius (Event Horizon) The idea that a black hole has a “radius” seems like a strange thing to talk about, remember a black hole is defined as an object that is infinity small (radius → 0). This radius is not so much a physical Singularity boundary but the distance from the center of the black hole where the escape velocity is equal to the speed of light. Everything within that radius (Schwarzschild Radius) or Event Horizon is trapped and can never escape. Schwarzschild Radius Schwarzschild Radius Equation: 2퐺푀 푅푎푑푖푢푠 (푚) = 푐2 푁∙푚2 G = Gravitational Constant (Big G, 6.67푥10−11 ). 푘푔2 M = mass of black hole (kg). 8 c = the speed of light (3x10 m/s). 1 M☉ = 1.989x1030 kg We can simplify the expression by substituting in all the constants and recalculate: Schwarzschild Radius (km) = 3 M☉ (mass in solar masses) Black holes can vary in “size” by the amount of mass they contain. Some of them can get mind- blowing big. Distance to Neptune is ~30 AU (4.5 billon kilometers). Black hole Classification Classification Mass Radius* 5 10 Supermassive black hole 10 to 10 M☉ 0.001 to 400 AU Intermediate mass ~1000s M☉ ~1000s km Stellar black hole 10 M☉ ~30 km Micro black hole Up to the mass of the Moon Up to 0.1 mm *The black hole itself is infinity small, the radius is referring to the size of the event horizon. Table 3: Classes of Black Holes Black Holes - 5 .