I finally graduated and got my Master's degree (with full marks, fuck yeah!), so to celebrate i decided i'd write another blog on astrophysics. I already wrote a basic introduction a while ago (found here: http://www.teamliquid.net/blogs/483814-a-basic-introduction-to-astrophysics), so this time around i'll focus on the stuff i've done research on instead.
Black Holes
In a nutshell, my specialty is black holes. A black hole is, to put it simply, a single point in space where a certain amount of mass is sitting. If you think about it this already doesn't make any sense: even subatomic particles have a certain physical dimension, and it's completely nonsensical to think that a ton of them can all be at in the same exact point in space...indeed, we have no idea of what actually happens inside a black hole, but we do know that General Relativity, the most accurate theory of gravity we have been able to write, predicts both their existance and how they affect their surroundings; every time we've been able to test its predictions, they have been spot on. For a theory that is over 100 years old, that is really impressive.
The actual equation required to study a black hole is called Einstein's field equation, and it is the basic equation of all of General Relativity. It also looks really fucking scary:
Honestly i haven't had to work with it in about two years and i don't really remember how to solve it off the top of my head, i just posted it to brag. Fortunately, it is possible to grasp what a black hole does even using simple classical physics. Imagine a particle of mass m travelling at the speed of light (the highest possible speed achievable in nature). It's kinetic energy will be 1/2 m c^2. Now imagine it is moving inside the gravitational field of another mass M; its binding gravitational energy will be GmM/R We can equal the two, to find a specific radius at which the particle requries a velocity of exactly c to escape the bigger mass:
1/2 m c^2 = GmM/R, which gives us
R = 2 GM/c^2.
This radius is called the Schwarzschild radius, or event horizon. What it means is, if you have a point-like mass M and you pass at a radius closer than the Schwarzschild radius, even light can not escape, as the velocity required to leave is higher than c, which is the highest possible velocity anything in nature can achieve. The higher the mass M, the larger the radius. For an object with the same mass as the Sun, this radius is 3 km, which is considerably less than its actual size. In other words the Sun doesn't have a true event horizon, because it's not a point-like mass, but it is extended over a radius of about 700000 km. However, suppose you could somehow, someway compress the entire Sun within 3 km; in that case, it would have a Schwarzschild radius, turning it into a black hole. Black holes are ridicolously dense objects; they need to contain the entire mass of a star in a really, really small volume.
Two kinds of black holes
We know of two kinds of black holes in nature: stellar mass black holes, and supermassive black holes.
Stellar mass black holes as the name implies are about as heavy as a star, and they are born when a particular kind of star ends its life. The way a star functions is fairly simple in principle: they are big spheres of self-gravitating gas. In order for the star to be stable, some amount of internal pressure is required to keep the gas from falling on itself due to gravity. In a typical star, this is caused by the nuclear reactions happening in its core: the energy they release "pushes" outwards, balancing gravity. When a star isn't capable of nuclear reactions anymore however nothing opposes gravity, and the gas can collapse. In some situations, there is a quantum mechanical effect called degenarcy pressure that eventually stops the collapse and stabilizes the star, but sometimes even that isn't enough, and most of the gas in the star keeps falling towards the core. When this happens, a black hole is born.
We observe stellar mass black holes in a particular kind of system, called X-ray binaries. A good portion of stars aren't born alone, but they have a twin companion. If one of the two stars in the binary system becomes a stellar mass black hole, it can start devouring the outer layers of its companion because of its gravitational pull. As the gas falls onto the black hole (the technical term is, the gas is accreted by the black hole) it is heated to extreme temperatures, and ends up emitting very brightly in X-rays which some satellites like XMM-Newton, Chandra, NuStar and Swift can observe.
The other kind of black holes, which are the ones i work on, are called supermassive black holes. Their mass is between a few million and tens of billions times the mass of the Sun, which is way, way more than any single star could ever achieve. We aren't really sure where they come from, but we do know that they can't come from a stellar mass black hole that has accreted enough gas to grow to extreme masses. This is because a black hole can only eat so much mass at a time; there is a limit to accretion, called the Eddington limit. As gas is accreted, it needs to dissipate its energy in some way, otherwise its orbit will never approach the Schwarzchild radius. This is what originated the emission we observe from black holes. However, light can exert a force on matter, pushing it away. The more matter falls, the more light is emitted, the more matter is pushed away. Therefore, there is a limit to how fat a black hole can get in a given time. Supermassive black holes are observed up to very far distances, which corresponds to very short times after the Big Bang. This gives them a very short time to grow to their extreme masses, too short for their original mass to be close to a star's. Their origin is one of the great mysties of modern astrophyics. Almost every galaxy in the universe, inlcuding ours, hosts exactly one supermassive black hole in its center.
Active Galactic Nuclei
Supermassive black holes do not typically contribute to the light we see coming from a galaxy...they are in the middle of nowhere and light can't escape from them anyway, so why would they? About 1% of the time however something wierd happens: the core of the galaxy appears way brighter than it should be. In this case, we say that the galaxy hosts an active galactic nucleus, or AGN. Like in X-ray binaries, this happens when supermassive black holes have a disk of gas surrounding them; as the gas is accreted, it emits light. AGN accretion disks aren't as hot as those in X-ray binaries, so they emit mainly at optical and ultraviolet frequencies, rather than X-rays. The brightest, baddest AGN are called quasars, and they outshine their entire host galaxy: we only see the emission of the core region, despite the fact that it isn't much bigger than the solar system. We know the emission region is that small, and therefore the emission can only be produced by something as compact as a black hole, because of a simple argument. AGN are very variable sources; their luminosity can change drastically over years, months, days or even minutes in the most extreme cases. Because information can not propagate faster than the speed of light, if we see an object varying over a time t we can roughly estimate its size R: t = R/c. It can not be bigger, otherwise it would take longer to vary any property, such as luminosity.
In about 10% of the AGN, not all the gas falling onto the black hole crosses the event horizon. Some of it is instead launched away from the black hole in two jets of plasma which move at close to the speed of light. These jets are some of the largest structures observed in nature, as they can reach sizes that are tens of times the typical size of a galaxy. AGN jets are some of the brightest objects in the sky at basically every wavelength; they are observed as far away as 12 billion light years away from us.
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AGN are tightly connected to the galaxy that hosts them; the two evolve together over time. On the one hand, the galaxy's gas needs to somehow be sent towards the central region in order to trigger accretion, which requires some kind of "traumatic" event happening to the host galaxy. Typically, orbits of stars and gas clouds in a galaxy are very stable, and it is not simple to figure out exactly how so much gas ends up in the central region. As far as we know, there are two kinds of events that can make this happen. The first is some kind of instability appearing in the galaxy itself, without any external trigger. This happens in spiral galaxies like the one in the image below, in the left galaxy: instead of following the galaxy's spiral arms, stars and gas enter peculiar orbits which appear as a bar-shaped structure near the center. Bars are inherently unstable, and they can channel any gas that enters them towards the center, where it will be swallowed by the central black hole. The second kind of trigger is mergers between two galaxies. Mergers can very easily disrupt the orbits of a galaxy's components, and again, the result is that the gas is sent towards the center region. This is how a galaxy can trigger an AGN. Once an AGN is triggered in turn it affects how its host galaxy evolves. Accretion and jets are extremely bright and violent phenomena, much more so than nuclear reactions; part of the energy they emit can be re-absorbed in the host galaxy, blowing away any gas cloud that could otherwise have formed new stars. This process is known as AGN feedback, and without it we couldn't explain the star formation history of the universe: without it, there would be too much star formation in any galaxy, too many young stars which are not observed in reality.
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I won't go into detail of the mechanics of AGN and jets, which is what my thesis and future research is about, but if you have any questions ask away!
Thank you for another interesting astrophysics blog.
In your derivation of the Schwarzschild radius, you expressed the kinetic energy of an object moving at the speed of light as .5 m c^2. Why did you neglect special relativity and specifically gamma in this part of the derivation? Obviously if you did not neglect gamma you would find that the kinetic energy of that object is infinite, and therefore the Schwarzschild radius would have to be 0, but how is it physically valid to use the classical equation for relativistic speeds?
On July 01 2016 09:44 micronesia wrote: Thank you for another interesting astrophysics blog.
In your derivation of the Schwarzschild radius, you expressed the kinetic energy of an object moving at the speed of light as .5 m c^2. Why did you neglect special relativity and specifically gamma in this part of the derivation? Obviously if you did not neglect gamma you would find that the kinetic energy of that object is infinite, and therefore the Schwarzschild radius would have to be 0, but how is it physically valid to use the classical equation for relativistic speeds?
And why is the rotational energy excluded? In engineering, kinetic energy of a rigid body is typically 0.5m*v^2+0.5*I*omega^2.
My question is what makes galaxies travel in galaxies, because if the argument is gravity brings the dust together, then it still doesn't explain the increasing expansion of the universe. I know it's kind of an unsolved problem, so asking you isn't exactly fair, but...
I suppose it brings me to the second point/question - when learning and researching what you're doing, how confident do you feel that you are right. I've enjoyed researching some stuff as a pastime, and more often than not, the theory was some jumbled mess, the in some way represented what reality did. Kind of the same thing with the standard model, it's so ugly... But the ideal case in more or less every engineering discipline I've seen has an elegant solution, it's only once you start accounting for effects that are absurdly tough to quantify (such as turbulence in fluid flow), does the result no longer have an elegant solution... But you see where that error comes from.
So yeah, just wondering on your stance on that, because that was the downfall I always had when I got excited with astrophysics (maybe you have some answer for me to my initial question, and you can disregard everything I said ).
Anyway, I appreciate the article, interesting stuff like last time! (however my preference is more science instead of describing what we observe, I prefer the why of it more, but I'm likely in the minority).
Something that always bothered me about the description of black holes is the seeming contradiction between having mass concentrated in a single point together with the idea that matter approaching the event horizon will freeze in time (seen from an outside perspective). When a black hole forms, wouldn't it in theory stay frozen and uncollapsed until infinite time has passed for an outside observer? And wouldn't that also mean that black holes with point-like mass don't really exist?
Or is the point-like description of a black hole used because its effects are observationally identical to a more spherical distribution of mass but easier to calculate?
On July 01 2016 17:17 stenole wrote: Something that always bothered me about the description of black holes is the seeming contradiction between having mass concentrated in a single point together with the idea that matter approaching the event horizon will freeze in time (seen from an outside perspective). When a black hole forms, wouldn't it in theory stay frozen and uncollapsed until infinite time has passed for an outside observer? And wouldn't that also mean that black holes with point-like mass don't really exist?
Or is the point-like description of a black hole used because its effects are observationally identical to a more spherical distribution of mass but easier to calculate?
We don't really have any idea what is happening behind the event horizon.
On July 01 2016 09:03 Impervious wrote: This is pretty fascinating stuff. Is there any "light" reading you would recommend for people wanting to learn more about it?
I can't really think of any specific book that you could find right now; i have a few that were written by an italian astrophysicst called Margherita Hack, but i don't know if they've ever been translated in English.
On July 01 2016 09:44 micronesia wrote: Thank you for another interesting astrophysics blog.
In your derivation of the Schwarzschild radius, you expressed the kinetic energy of an object moving at the speed of light as .5 m c^2. Why did you neglect special relativity and specifically gamma in this part of the derivation? Obviously if you did not neglect gamma you would find that the kinetic energy of that object is infinite, and therefore the Schwarzschild radius would have to be 0, but how is it physically valid to use the classical equation for relativistic speeds?
That mass includes special relativity, so it's gamma*m0, where m0 is the rest mass and gamma the Lorentz factor of the particle. I just didn't include it for simplicity.
On July 01 2016 14:38 FiWiFaKi wrote: And why is the rotational energy excluded? In engineering, kinetic energy of a rigid body is typically 0.5m*v^2+0.5*I*omega^2.
If you include the rotational energy of the black hole you find a slightly different solution with a smaller event horizon, called the Kerr solution. If you really want to do it properly you should use the field equations anyway (which are the relativistic equivalent of the Poisson equation), in which you can include or neglect angular momentum.
My question is what makes galaxies travel in galaxies, because if the argument is gravity brings the dust together, then it still doesn't explain the increasing expansion of the universe. I know it's kind of an unsolved problem, so asking you isn't exactly fair, but...
If you mean what makes the universe expand, yes, we do not know really, we just know that it started in a very hot and dense state, and that it's been expanding and cooling since. This is another of the predictions of general relativity which (with some caveats) is reproduced perfectly by observations.
We do have a decent idea of how galaxies form though. Imagine that the distribution of matter in the early universe, slightly after the Big Bang, isn't perfectly homogeneous, but instead there are some fluctuations around the average value: in some places there is more density, in otheres there is less. The zones with the highest densities have more matter in them, so they also attract stuff surrounding them more strongly than zones with low densities. Simply because of gravity, you'll have zones that end up having tons of matter in them, which eventually collapses to form stars, galaxies, groups and clusters of galaxies, and super clusters, and huge voids that started as slightly less dense than the average, but eventually are basically completely empty of anything, which is exactly how matter is organized in the universe on very large scales.
I suppose it brings me to the second point/question - when learning and researching what you're doing, how confident do you feel that you are right. I've enjoyed researching some stuff as a pastime, and more often than not, the theory was some jumbled mess, the in some way represented what reality did. Kind of the same thing with the standard model, it's so ugly... But the ideal case in more or less every engineering discipline I've seen has an elegant solution, it's only once you start accounting for effects that are absurdly tough to quantify (such as turbulence in fluid flow), does the result no longer have an elegant solution... But you see where that error comes from.
So yeah, just wondering on your stance on that, because that was the downfall I always had when I got excited with astrophysics (maybe you have some answer for me to my initial question, and you can disregard everything I said ).
Well, simple and elegant aren't quite the same thing. General relativity is very, very elegant, but it definitely isn't simple, and it's natural that the more effects you have to account for, the more complex stuff is.
Ultimately, nothing in science has THE perfect answer to everything accounting for every detail. That's just imposible. What you do is make some assumptions at first, which lead to approximations, and you see where those assumptios lead you. Within that set of assumptions, if you didn't fuck up, your math model predicts reality...the tricky part is to understand if your set of assumptions corresponds to something that is realistic or not.
Anyway, I appreciate the article, interesting stuff like last time! (however my preference is more science instead of describing what we observe, I prefer the why of it more, but I'm likely in the minority).
Unfortunately it's kind of hard to do that because once you start writing equations you risk being way less understandable, especially on TL.
On July 01 2016 17:17 stenole wrote: Something that always bothered me about the description of black holes is the seeming contradiction between having mass concentrated in a single point together with the idea that matter approaching the event horizon will freeze in time (seen from an outside perspective). When a black hole forms, wouldn't it in theory stay frozen and uncollapsed until infinite time has passed for an outside observer? And wouldn't that also mean that black holes with point-like mass don't really exist?
Or is the point-like description of a black hole used because its effects are observationally identical to a more spherical distribution of mass but easier to calculate?
The point-like description is an assumption you make to have a simpler equation to solve. If you look at the field equation at the top, it makes the left hand side term disappear. That said, it is reasonable because if nothing can stop gravity, on paper everything should collapse to a very tiny scale.
The issue of matter approaching the event horizion is a very mathy problem. Basically, you can find a set of coordinates which allows matter to be seen crossing the event horizion in a finite time by any observer; it's all about writing the problem "correctly" if that makes sense. Once something cross the event horizon, its only possible trajectory is forced to fall to the center, but by this time it can no longer communicate with observers outside of the black hole.
The point-like description of a black hole is used because, as i said, we do not know of anything that could stop the mass from collapsing to a point, once density is past a certain limit. There are wierd solutions of the field equations that actually do not predict a point-like mass, sometimes including quantum mechanics effects like quark stars, gravastars and other badass names like that, but i don't know anything about them. Regarding my specific research, the mechanics of gas accreting are always derived by using the Kerr or Schwarzschild solutions.
On July 01 2016 17:28 Alluton wrote: We don't really have any idea what is happening behind the event horizon.
Slightly incorrect, we can not communicate or test anbything the event horizion, but GR's equations are just as valid inside of it as outside. The only place where every equation we know, GR and quantum mechanics included, blows up and loses any meaning, is the center point-like mass, because we are assuming density becomes infinite.
Really enjoyed reading about this. Black holes are fascinating because we actually don't know everything about them, and that part of mystery is actually attracting to me.
Also, didn't know about the Schwarzschild radius. It's quite amazing how it transforms a pretty spectacular and unbelievable particularity of black holes ("even light can't escape") into something that's actually sensible and sound, explained in a rather simple equation (by that I mean it's not covering two black boards).
On July 01 2016 22:07 deth2munkies wrote: So are AGN jets like super gamma ray bursters or something entirely different?
Admittedly all I have knowledge-wise is a boxed set of The Universe and a non-major Astronomy course.
The physics are very similar, but the scales are very different. It's fairly common for people (my supervisor included) to work on both. In both cases, we are observing a jet of relativistic plasma, usually moving towards us (in the case of gamma ray bursts especially). This is really important, because if an object is moving at close to the speed of light, the properties of the light it emits depend greatly on the angle from which we are observing: if the source is moving towards the observer, it appears much more brighter.
AGN jets have speeds between roughly 90 and 99.9% the speed of light (their Lorentz factors are between ~3 and ~20), they can be larger than the host galaxy hosting them, and they are seen up to redshifts of about 6-7, corresponding to roughly 12 billion light years.
GRBs can happen when a star ends its life, explodes in a supernova and its core collapses to a stellar mass black hole, or when two neutron stars (which are the last stage of the evolution of a binary system of two massive stars) collide. When this happens, part of the matter falling onto the black hole is accreted, and a jet can be launched, just like in an AGN or X-ray binary. The physical size of GRB jets is much smaller than an AGN, but they can be up to two orders of magnitude brighter because their Lorentz factors are between ~100 and ~500, which is absolutely fucking bananas (the faster an object, the brighter it can appear). This makes these sources way, way more violent and bright. GRBs are seen up to redshifts of about 9, which is about 13 billion light years away from us.
As I understand it, as a mass approaches the speed of light, you can no longer use the 1/2mv^2 equation and have to start using relativity. What's the new equation? How close to the speed of light do you have to be?
Also, how did you feel about the detection of gravitational waves?
As I understand it, as a mass approaches the speed of light, you can no longer use the 1/2mv^2 equation and have to start using relativity. What's the new equation? How close to the speed of light do you have to be?
Also, how did you feel about the detection of gravitational waves?
Sort of. As a particle with a mass m0 approaches the speed of light, its mass actually increases. The correct formula for mass, including special relativity, is m = g*m0, where m0 is the mass at rest (ie, when the particle isn't moving) and g = 1/(1-v/c)^(1/2). A particle's kinetic energy is usually written as K = 1/2 m v^2 = 1/2 m0 g v^2, which includes special relativity.
Gravitational waves are the biggest discovery in astrophysics in the last 87 years (the expansion of the Universe was discovered in 1929), it's absolutely mind blowing. It proves that black holes really do exist (no other object could produce the gravitational waves we observed), that they can merge together in a reasonably short time frame (which makes explaining the existance of supermassive black holes a bit easier), and that gravity really is described by General Relativity to an impressive level of precision.
On July 01 2016 22:07 deth2munkies wrote: So are AGN jets like super gamma ray bursters or something entirely different?
Admittedly all I have knowledge-wise is a boxed set of The Universe and a non-major Astronomy course.
The physics are very similar, but the scales are very different. It's fairly common for people (my supervisor included) to work on both. In both cases, we are observing a jet of relativistic plasma, usually moving towards us (in the case of gamma ray bursts especially). This is really important, because if an object is moving at close to the speed of light, the properties of the light it emits depend greatly on the angle from which we are observing: if the source is moving towards the observer, it appears much more brighter.
AGN jets have speeds between roughly 90 and 99.9% the speed of light (their Lorentz factors are between ~3 and ~20), they can be larger than the host galaxy hosting them, and they are seen up to redshifts of about 6-7, corresponding to roughly 12 billion light years.
GRBs can happen when a star ends its life, explodes in a supernova and its core collapses to a stellar mass black hole, or when two neutron stars (which are the last stage of the evolution of a binary system of two massive stars) collide. When this happens, part of the matter falling onto the black hole is accreted, and a jet can be launched, just like in an AGN or X-ray binary. The physical size of GRB jets is much smaller than an AGN, but they can be up to two orders of magnitude brighter because their Lorentz factors are between ~100 and ~500, which is absolutely fucking bananas (the faster an object, the brighter it can appear). This makes these sources way, way more violent and bright. GRBs are seen up to redshifts of about 9, which is about 13 billion light years away from us.
On July 02 2016 08:48 Teoita wrote: Which part did i not explain well?
It's not explaining, it's just I have no freaking clue what Lorentz factors are. I feel like I knew at one point and am fairly certain it has to do with that brightness scale we used in Astronomy but I don't remember anything about it
Otherwise excellent, I learned some new things today, so thank you.
On July 02 2016 08:48 Teoita wrote: Which part did i not explain well?
It's not explaining, it's just I have no freaking clue what Lorentz factors are. I feel like I knew at one point and am fairly certain it has to do with that brightness scale we used in Astronomy but I don't remember anything about it
Otherwise excellent, I learned some new things today, so thank you.
Ah, it's just how close to the speed of light something is going. As i said, if something is moving towards you at the speed of light, it appears brigther than it actually is, because instead of emitting in every direction, it emits towards the direction of motion, like in this pic:
EPT
![[image loading]](http://i.imgur.com/TwGFSbk.jpg)
![[image loading]](http://i.imgur.com/n9GmAdw.png)
![[image loading]](http://i.imgur.com/l8chy0J.jpg)
![[image loading]](http://i.imgur.com/DaELpiV.jpg)
]![[image loading]](http://www.teamliquid.net/staff/Teoita/Hubble/rosegalaxy600v2.jpg)
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![[image loading]](http://math.ucr.edu/home/baez/physics/Relativity/SR/Spaceship/Aberration.jpg)
