Saturday, 10 October 2015

Looking at a Black Hole

 Hello and thank you for looking at this post. If at any point you begin to feel overwhelmed, please, it's not you, it's me writing in a way that's too sophisticated. It's my fault.
 If you are familiar with Black Holes, maybe you don't need to read through this post at all and you can do something else with your time.
 If you are not and haven't read much about Black Holes, then you might want to read slowly and ponder on some of the finer moments. I will try to provide information as scientifically correct and pictorial as possible. Please note, that at times it might be good to additionally Google some term.
 If you know much about Black holes, but are not sure if you're missing details, then check it out; something interesting might pop up.

 Looking at a Black Hole

1. A bit of Info

 Black Holes, a.k.a. Singularities(there are various types of Singularities; the Big Bang being one of them) are made entirely of curved and warped space-time. They begin as matter but have no matter once they become black. The large round black spheroid we all are used to imagining when thinking of a Black Hole is the Event Horizon, the point after which not even light can escape. Being trapped and orbiting inside it never reaches our eyes, hence the area is also the shadow of the Singularity Black Hole(imagine an infinitesimal point in space which casts a shadow in all directions).

 There isn't a particular known mass at which a star would degenerate into a Black Hole, but an assumption is just over forty solar masses(that is 40 of our Suns packed together), although throughout the life of a star many things can influence the flow of matter in or out. So even if a star has critical weight it might not compress into a Singularity but instead settle down to a Magnetar(Neutron Star with a very powerful magnetic field).
 The fusion of Hydrogen, Helium and heavier elements in stellar cores is powered by gravity in the beginning. Once the Star ignites, the thermonuclear reactions are pushing outwards, while the gravitational forces are "squeezing" in. Once the fusion cycle reaches iron, there is no more energy released when fusing elements(from this point on it takes energy to fuse them). A cycle can end before that, by shedding the upper layers in an explosion(not supernova) and leaving the core to continue its life cycle. The upper layers--the bulk of a star we see, are made from plasma(the fourth physical state of matter and the one that is most abundant in the Universe) which is flowing much like a lava lamp, rising and cooling, sinking and heating.
 Every star goes through this cycle. The upper layers are shed once there is not enough fuel to push outward. Gravity focuses on the core and leaves the rest to become stellar dust, which will feed new stars and/or planets...hopefully. 
 The left core is in a state of a White Dwarf--a tea spoon weighs fifteen metric tons. The famous quantum law of Pauli's exclusion principle states that a particle cannot occupy the same position as another particle. In a form of a White Dwarf there are seas of electrons bustling around. Though squeezed tight, together with the atomic nuclei they form the body of the Dwarf Star. If the force of gravity is not powerful enough, the dwarf will live in a state of equilibrium for a very long time. The least assumption is one with thirty two zeroes behind it in years.
 There is still much power left and energy will be released; a magnetic field will form. If gravity is sufficient enough it will crunch the electrons out of their orbits and produce supernova(there are various types dependant on the strength of the supernova). This is when heavier elements get fused together and for the larger part, the biggest source of Uranium in the Universe.
 The crunched electrons will fuse with protons and form a degenerate matter made predominantly of neutrons. A neutron is heavier than a proton(and can decay into a proton by emitting an electron and an electron anti-neutrino or a positron and an electron neutrino--not so important!). In either case it loses mass and energy. 
 This is a state of a Neutron Star--one tea spoon weighs ten million metric tons. These are much smaller than their White Dwarf partners. They spin, most of the time vehemently and emit radiation and so earned the name pulsars, because in the early days of radio astronomy scientists were puzzled by these "cosmic lighthouses".
 Alas, if gravity is powerful enough, the state of a Neutron star lasts only for some seconds. If the crunching continues, the entire mass will get smaller and smaller until it vanishes from sight. Observed from far away it will be as if it has faded from view. Steadily the Event Horizon will emerge--the shadow of the Hole. Its size depends on the mass of the matter being "crunched" together.
 Now there is no matter to speak of any more. The entire Singularity is formed of curved space-time into infinity. The current understanding of physics calculates infinities when trying to resolve numerically the state of the Singularity. This means that we don't really know what's at the centre (although there are some very interesting speculations!).
 To make things a bit more pictorial, imagine you standing in your back yard with a wide net stretched thin. You throw a stone as hard as you can and the stone bends the net, for a moment the two dimensional plane of the net is "twisted". It has curved into a three dimensional object. For a tiny ant living on the two dimensional plane of the net, it might seem that the plane is still flat when it is walking about, but to us--we see the entire picture easily.
 Of course, after a short time, the net will push the stone back and it will return to it's state of minimum energy(being stretched and at rest). But imagine if the stone was stretching the net into infinity. Look at this picture to help you imagine.

 From the perspective of a two spatial dimensions we can easily imagine what exponential curve of space looks like. Now try to think about what an infinite curve would mean in three spatial dimensions, like our universe.
 Having difficulties? No worries. Science also has not evolved enough to make absolute sense out of it. For all we know, we have not yet observed a Black Hole(or rather its Event Horizon) directly.
 The last boring information I will add before continuing is that unlike the net from our earlier scenario the Black Hole Singularity will take a lot more time to "unfold". Physicist Steven Hawking predicted that Black Holes evaporate slowly, but that is to be confirmed by observations in the future. His name will probably be awarded with a Nobel prize in the future.
 Also, unlike the net, the Singularity is staying in this "maximum" state of curvature, simply because it is in a "maximum" state of curvature. That is, the twisted space-time is supporting its own structure, despite the enormous energies involved into "folding" it in the first place. The stone is staying in the net, stretching it into infinity and you don't know exactly how far away that is from you.

 2. Looking at a Black Hole

 Like the stars they are born from Black Holes can spin. They can also be at rest--no spin. In Physics spin comes in two variations. Fold the palm of your right hand in a bowl and extend the thumb up. It is accepted that a body that follows the directions of your four fingers while spinning is spinning up--that is, its torque is pointed in the direction of your thumb. The opposite direction would be spin down, because for your fingers to follow the direction of the spinning body you'd have to turn your thumb up side down. This is what they mean in Quantum Mechanics when they say spin up and spin down. The same applies for a Black Hole.
 Let's talk about Spinning Black Holes for a bit. 
 Now, there is a theoretical maximum spin that a Black Hole can retain, according to the currently established laws of Relativity. But for that I'll need to dump a bit more information. I do apologize.
 We already discussed that light does not escape out through the Even Horizon, but there is one other very important characteristic of space-time when it is curved to such extremes. It is flowing much more slowly as observed from a distance. We see the same effects in our every day life. Relativity is part of Nature and our personal local time runs quicker when we're on the tenth floor, than when we're in the basement. Studies have been made with very precise atomic and caesium clocks to reveal different flow of time between such ordinary places. Of course, the differences are very small here on Earth, but none-the-less perceivable. So when we're closer to the central gravitational well at the centre of the Earth, as in the basement or ground floors, time runs slower from the point of view as when we're on the tenth; space-time is slightly more curved than it is at the tenth floor. An interesting fact is that the satellites of the GPS system have to calculate time according to the relativistic laws, otherwise your GPS location on your phone would jump to the middle of the ocean after a week. That's how noticeable the differences accrued can be between space out there and here on Earth. 
 Back to the super curvature around a spinning Black Hole. The spin actually increases the slowing of time additionally. If you were to orbit a super-large super-fast-spin Black Hole in your space ship, you'd walk around normally and drink your tea and everything will be OK, except that time outside of the extreme space-time curvature is flowing much more quickly from your point of view. In some cases an hour in your ship measures to years of outside time. And as absurdly as it sounds, you don't have to worry that much about falling into the Hole either. When a Black Hole is spinning it pushes space time in the direction of it's spin, be it spin up or spin down. So that things will orbit around the Event Horizon accumulating centrifugal forces which will push them around the Black Hole. Things in Nature always move in straight lines. It's just that space-time is always terribly curved in Nature(stars, planets, galaxies, Black Holes ect.). That's why your ship will be orbiting in the direction of the spin of the Black Hole. Every particle, object or ship, especially photons of light(carriers of visual information) will either orbit around the Black Hole, together with it's spin and thus increasing it's spin because of their accrued centrifugal forces. Or they will try to orbit in the opposite direction, if they are unfortunate enough to enter the system from the wrong side. When they try to orbit against the spin, they will slow down the spin a bit, but will be plunged into the Hole, because they will lose all centrifugal forces, thus depleting their angular momentum and their energy will fail to overcome the extreme gravity. So they will sink underneath the Horizon. When an object does, the last thing we see is its image staying there for a while, especially if we're observing from afar(it will wear off quicker the closer we're orbiting). Part of the photons(carrying the image) are trapped just outside of the Event Horizon and are dragged by the whirl of space-time. Now the image is frozen and is spinning together with the Black Hole and the speed of it's spin is the speed at which the image would orbit around the Black Hole. There's nothing much to sparkle the imagination here, unless the speed of the object goes beyond the speed of light(nothing can travel faster than light according to Relativity). In some, surprisingly, not-so-rare cases an ultra-large Black Hole--one hundred million masses of our sun and above, can approach such spin speed. Such a Black hole would have a diameter as close to that of the Earth orbiting around the Sun. And an image of an object orbiting such an Event Horizon would make that orbit in between one and two hours! If the speed were to exceed that of the speed of light, theoretically, the Event Horizon would disappear and we will be able to see a naked Singularity. So far, science predicts that is impossible, but one never really knows. Current estimation calculates that when a spin of 0,998 of the maximum possible is reached a state of equilibrium would ensue between particles speeding up the spin and particles slowing down the spin.

 What is important to take from all that info-dump is that Photons of light(carriers of visual information) would travel in extremely bend straight line around a Black Hole. It would change the image that we'd see, if we were ever to observe an Event Horizon directly. 

 A star behind a Black Hole can even appear twice in the sky depending on our point of view.

 Making things easier for you--now you know what a non-spinning Black Hole would look like as seen above. 
 If you take pen and paper and scribble quickly a twisted two dimensional plane into infinity as one shown above. The exponentiation twist is the Black Hole. Place a dot somewhere outside on the plane--that would be a star. Two straight lines coming from the star would depict photons, carrying its image to our eyes. The straight lines would bend just around the edge of the curvature and when exiting, their path would have changed so as to converge in our eyes. Thus we would see two stars. 

 First, I apologise for the non-interactive image.

 But it is worthwhile to look and think on the image for a bit. Here the Black Hole is spinning up(remembering the right hand rule, which direction is that?).
 The numbers on the flat disk run from zero to nine, but they appear in several other instances as well. That is because the curvature of space-time makes photon travel in unusual ways. 
 In this case we see several instance of number six, because the photon information for number six swirls around from behind the Event Horizon to our eyes in several rays. 
  You will notice that space-time is additionally curved in the direction of its spin. The high speed of the spin up is literally stretching space-time in the same direction and bulging it in the other end of the Event Horizon. To see this a bit more clearly.

 This picture was used by respected theoretical physicist Kip Thorne when constructing Gargantua in the movie Interstellar. It is showing the lensing of the curved space-time, which a massive Black Hole would produce. Plus a little bonus--how we will see space moving when changing our point of view from left to right. The red lines flow towards the right side of the screen--in this sector the view would change somehow normally. Inside the big purple line, called "Einstein Ring", the view would change in the opposite direction. The yellow arrows and the view flows to the left. 
 Compare that picture with the picture of the non-rotating Black Hole. Now you see what the massive spin would do to additionally drag space-time. 
 Since we have mentioned Gargantua and the movie Interstellar, why don't we just Google it in images and observe it for a bit.

 Magnificent isn't it? It is by far the most scientifically correct Black Hole to be presented in IMAX high-resolution image. But not even that is good enough. Christopher Nolan didn't want to confuse the public with a fully scientifically correct Gargantua. Instead the graphical team agreed to construct something less odd for the viewer despite the much needed massive gravitational forces to produce the drama in the movie.  
 To understand what the beautiful Gargantua is missing we might have to look at the mighty Quasar. 

 Quasar stands for quasi-stellar radio object. During the advent of radio astronomy it was puzzling to detect an object as small as the size of the solar system and shining brighter than the whole of the Milky Way Galaxy...or a hundred of them for that matter!
 Quasars are super massive Black Holes with high Spin(according to the right hand rule, what spin does the Black Hole in the picture above have?). Gravitationally, they are not unlike Gargantua, which has one hundred million solar masses. In reality this immense force would attract all sorts of objects in orbit. In the picture above an A type hot Blue-White Star is being slowly drained of its Hydrogen fuel to power an Accretion Disc around the super massive Black Hole in the centre, while the star itself is orbiting the Black Hole. Remember, that once the mass and spin of a Black Hole reach a limit objects in orbit do not tend to fall underneath the Event Horizon. Quasars produce immense magnetic fields which would hold the orbiting particles in place against the whirling space-time and gravity. This produces friction which heats the gas and particles of the Accretion Disk and emits radiation across the entire spectrum of light, from gamma rays to long radio waves.  Additionally, if any particles do fall under the Event Horizon their magnetic quantum stays there at the border. This magnetic energy accrues over time and drags hot dust from the Disk towards the spinning poles of the Quasar. Once a critical mass is reached the dust is ejected in a jet that can be many many light years long. The ejected dust can serve as the building blocks for new stars and planets. 
 There is something else that is missing from the beautiful images of Gargantua. Can you guess what it is? Look at the picture with red and yellow lines and think again.

 One last detail that is hard to come by is the effect of the Dopler shift. We see and hear it every day in our lives. When a car comes towards us its pitch is high; when it drives past us, its pitch is low. The sound waves in the front are compressed together and those on the back are stretched in the direction of motion. Hubble observed the so called "red-shifted" galaxies, which led him to believe that the Universe is expanding. This means that when those galaxies are flying away from us, their light waves get stretched and longer light waves correspond to the red spectrum of light. The approaching Andromeda Galaxy, in comparison is blue-shifted. 
 The same effect would be observed from the equatorial plane of a massive high spin Black Hole for its Accretion Disk. When spinning, the parts of the disk that come towards us would be blue-shifted and when spinning away from us they would be red-shifted.  

 Knowing all of these basic details and having looked at all those pictures, can you take five minutes away and imagine what a super massive Black Hole with high spin would look like. Do you want to draw it?
 I do.
 In fact, I asked an artist friend to help me with that, but he's busy this week, so we may do it next week. If he agrees to help I'll post the picture. 
 Thank you for taking your time to read through all of that not-so-important information. I appreciate it!