Black holes are the densest objects in the Universe. Their gravity is so strong, not even light can escape its pull, turning them into unfathomably dark wells of gravity. There are many open questions surrounding the physics in and around black holes, so many questions in the area don’t have easy answers, but we do our best to say what we can.
Black holes are the dead husks of giant stars that ran out of fuel and exploded in giant explosions called supernovas. These explosions are some of the brightest things in the Universe and can be seen for billions and billions of light years. Counterintuitively, black holes themselves can also create extremely bright objects called quasars, which are superheated jets of gas being shot out of the region surrounding a black hole.
We also have answers related to stars in general, including their life cycles and gravitational pulls.
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The fundamental science shown in Interstellar is correct. Time does in fact run slower in high gravitational fields, so if they were down on the planet in high gravity and then returned to the spaceship, less time would have passed for them. The spaceship would indeed perceive time on the planet to be running slower and the planet would see time running faster on the spaceship. However, the magnitude of the slowing of time (about 60,000x) is vastly exaggerated. They would need to be much closer to the surface of the black hole for it to be that large (like basically at the surface) so it’s not realistic. We have observed the stretching of time due to gravity in satellites before though, so it is a real effect.
The line between “super” and “ultra” massive black holes is arbitrary, so you can draw it wherever you want (or wherever is convenient for marketing your discovery). There are some black holes at the centers of galaxy superclusters that have been labelled as “ultramassive” recently, which you can read more about here. A full catalog of the most massive black holes known is listed here, and if we use the arbitrary threshold of 10^10 solar masses for “ultramassive” black holes, then there are about 30 we know of.
Usually when people talk about the radius of a black hole, they mean the size of its Schwarzchild radius, which is the closest light can get before it can’t escape the black hole’s gravity. This can be calculated with a surprisingly simple equation that scales with the mass of the black hole, and the radius of the black hole at the center of the Milky Way is only about 1/5th the size of the orbit of Mercury. If we want a black hole that has a radius the orbit of Pluto (one way you could define the edge of the Solar System) then you would need a black hole with a mass 2 billion times that of the Sun, or around 500 times the mass of the Milky Way’s black hole. If you want one that is 1 light year in radius (about the largest estimate you could give of the size of the Solar System), then you would need a mass of about 4 trillion Suns (or 1 million Milky Way black holes).This would be comparable in mass to the entire Milky Way galaxy, but galaxy superclusters are usually almost 1 quadrillion Suns in mass, so it would still only be a small fraction of its overall mass.
Black holes are strange objects that make most normal theories of physics break, so most of the time when we talk about black holes, we choose to instead talk about the event horizon. As you may have discovered in your research, the event horizon of a black hole is the threshold in space where the black hole’s gravity becomes too strong for anything to escape. The escape velocity there is defined in the same way as it is for anything else: it is the speed you would have to go in order to break out of the gravitational pull of the object. There are no fancy or exotic forces at play surrounding a black hole, just gravity, so when you get close enough to the surface that the gravity is so strong that the escape velocity is the speed of light, then that is the event horizon. Inside of there, a lot of physics gets messed up, so we’ll just talk about the edge.
Hawking radiation (another strange concept that goes against a lot of physical intuition) says that regardless of the fact that nothing should be able to escape, black holes constantly give off tiny amounts of energy. This can be thought of in a few different ways. One relies on the notion of pair creation, where a particle and an antiparticle can spontaneously appear out of nothing but energy in the middle of space. This has been proven to happen constantly around in the Universe (so there are constantly electrons and positrons being created around you all the time). Most of the time, these particles immediately smack back into each other and turn back into energy, but if these particles happen to be created right at the edge of the event horizon, one of them may have the energy necessary to escape, while the other falls back into the event horizon and into the black hole. Because these particles were created with energy from the black hole, the escaping particle represents a loss of energy for the black hole.
Another way of thinking about this is to think of it as quantum tunneling. In quantum physics, particles are represented as waves, and any wave has a chance of making it past a barrier it comes up against (think of this as sound waves getting through a wall; some get through but most are blocked). For higher barriers, the waves have less of a chance of making it through, and the event horizon is a very very high barrier so almost nothing ever makes it through. However, in the rare occasion a wave makes it through the barrier, that represents a particle making it out of the event horizon and thus the black hole losing energy.
So now we can talk about how the temperature of a black hole is even defined. For astronomical objects like stars, temperature is often defined by how much light it gives off and in what colors. The more energy they give off, the hotter we say the object is. You can see this in the difference between a smoldering fire that glows a dim red and a hot fire that shines bright white or blue. The only energy that a black hole gives off is Hawking radiation, so the temperature is defined based off of that. However, Hawking radiation is tiny, and as black holes get bigger, they give off less and less Hawking radiation, so real black holes have extremely cold temperatures. For instance, a black hole the mass of the Sun would have a temperature of about 6 * 10^-8 K and the black hole at the center of our galaxy has a temperature of about 10^-14 K!
One interesting consequence of this is that black holes are literally colder than the Universe. The cosmic microwave background is a constant bath of energy from the early Universe that bounces around everywhere in space. It has cooled over time as the Universe has expanded, but it still has a temperature of 2.73 K, warmer than any black hole with a mass greater than that of the Moon. So the empty Universe is giving more energy to black holes all the time, and since black holes give off less energy the bigger they get, they just keep getting colder. This process will only stop once the Universe cools to be colder than the temperature of black holes and then the black holes slowly evaporate with minuscule amounts of energy. That should happen in about 10^100 years or so.
Let’s start with just the Milky Way. We can tell that there is a black hole at the center of our galaxy just by looking at the stars orbiting around the center of the galaxy. For the last ~20 years, astronomers have been tracking stars in the area and have seen them zipping around some invisible object at incredibly high speeds. Using what we know about gravity from our own solar system, we are able to calculate the orbits of these stars and determine that it weighs about 4 million times as much as the Sun. There is no other object that could have that mass but give off no light, so it must be a black hole.
Moving on to other nearby galaxies, we see evidence of black holes in the form of active galactic nuclei (AGN). A galaxy with an AGN usually has some amount of light and material emanating from the center of the galaxy where the black hole is. To understand why, we have to think about what is going on around a black hole. Gas that is in the vicinity of the black hole is frequently condensed down into a flat circle of matter orbiting quickly and closely around the black hole (think Saturn’s rings except it’s massive amounts of gas). When some of this gas enters the black hole, it speeds up immensely as it falls in, and friction with other gas around it makes it incredibly hot, leading to it glowing very brightly. The huge amount of light blows out a lot of the other gas around the black hole, forming the jets that we see in the picture above. We see many such galaxies around us with varying levels of activity (corresponding to varying levels of gas), and we know that nothing else could make such a big and bright jet, so they must have black holes.
We can see similar effects clear across the Universe in the form of quasars, AGNs that are accreting tons of gas and are thus extremely bright. Quasars can be thousands of times brighter than the galaxy they live in, meaning they can be seen from very very far away (the furthest one we have seen is 29 billion light years away). They can be especially bright when their beams of ejected matter are pointed at us (these are called blazars). Similar to AGNs, nothing else can explain the brightness of a quasar other than huge amounts of gas falling into a black hole, so we know that even galaxies in the early Universe must have had black holes.
There are other lines of evidence that can be followed (simulations of galaxy formation don’t produce correct results without black holes, we can see black holes in the centers of some galaxies with radio waves, etc.), but the point is that we have observed a lot of supermassive black holes. Astronomers have not catalogued that there is indeed a supermassive black hole at the center of every single galaxy in the sky, but at this point, that is the conclusion that makes sense.
This idea of “rewinding” the expansion of supernova remnants has long been used to determine how long ago they exploded, and the process is roughly explained here. Astronomers have used this to match up existing supernova remnants to historical records from ancient astronomers who saw the actual explosions hundreds or thousands of years ago, which allows us to know more about the system as a whole. As long as you can measure the expansion speed and the distance (which are not always easy things to determine but are possible) then you can figure out roughly how long it has been expanding by running a computer simulation of the process.
Since Betelgeuse is so far away, the light that is reaching us now tells us what actually happened ~600 years ago. So it is possible that Betelgeuse already went supernova in its own reference frame, but we wouldn’t see that event until 600 years later since the light would take 600 years to reach us. Astronomers are actively making new observations and using models to infer the probability that we may see Betelgeuse explode. There are multiple ways to collect data on the nature of Betelgeuse’s explosion (if that happens/happened) — not just visible light, but also X-rays, radio waves, gamma rays (other “forms” of light), gravitational waves, and cosmic rays (high-energy particles like protons that travel at nearly the speed of light). It’s possible that some of these observations will be slightly delayed relative to others due to the nature of the explosion and/or variations in the interstellar medium along the line of sight to the supernova — that itself may help us learn a lot about the event.
The Oort cloud is a very poorly defined thing, existing only in theory and with very loose definitions. Generally, astronomers use the Oort cloud to encompass all of the orbital debris left over from the formation of the solar system that has been kicked far enough away that it is only bound to the Sun in the loosest way. This would theoretically extend out to the edge of the Sun’s gravitational influence, but where that actually is varies over time.
Barnard’s Star is about 6 light years away, a distance not too much larger than the Sun’s area of gravitational influence. However, Barnard’s Star is less than 15% the mass of the Sun, so its area of gravitational influence (called its Hill sphere) is only about half as large. So even using the absolute largest estimates, its Oort clouds probably doesn’t overlap with ours.
However, the gravitational effects of passing stars definitely effect Objects may have their orbits modified by passing stars and be kicked into other orbits (one theory of where comets come from). In the future, Barnard’s Star will be even closer to us, so it will stand a better chance of meaningfully influencing our Oort cloud. You may find this diagram of the distances to nearby stars over time interesting (using a more conservative estimate for the Oort cloud):
Another fun fact: the star Gliese 710 will pass only 0.178 light years from the sun in about 1.3 million years, definitely disrupting the Oort cloud and becoming the brightest star in the sky for a short amount of time.
Henrietta Swan Leavitt didn’t actually know the distance to the Cepheids she was observing, but she did know one thing: they were all the same distance away from her. She was very creative in her observations and chose to only study the Cepheids in the Small Magellanic Cloud, a satellite dwarf galaxy of the Milky Way that even at that time, astronomers realized was distant and cohesive. She knew that all of the Cepheids in the SMC would be the same distance from her (approximately), so she could isolate differences in brightness due to their periods and use that to generate a Period-Luminosity relationship. However, you are right that she was still limited by the rudimentary parallaxes of the time, so she was not able to turn her relationship into an absolute distance measurement before her death. It was only years later when Hertzsprung and Russell (two very famous names in stellar astrophysics) were able to measure parallaxes well enough to calibrate Henrietta Swan Leavitt’s distance measures and actually find out how far away the SMC was.