How to kick a Black Hole

ps200306

Later this year will be the fiftieth anniversary of the discovery of pulsars by Jocelyn Bell and Antony Hewish. They were the first of various compact stellar remnants that were purported to exist in theory, but for which observational evidence had been lacking. The idea of black holes was even more farfetched, although by the 1960s enough theoretical work had been done to convince most astronomers that they could exist in principle. (Einstein and others had believed that any real world object likely had too much angular momentum for a black hole to form because of the necessarily small radius). The discovery of the object called Cygnus X-1 was the first tantalising observational evidence for black holes.

Nowadays the evidence for black holes is overwhelming, especially with the advent of orbiting X-ray telescopes. Stellar mass black holes are "seen" when they form one companion in a binary pair. The stellar companion can be seen as a normal star, while the unseen black hole emits prodigiously at X-ray wavelengths. It's not easy to distinguish these from other X-ray binaries in which the compact companion is a neutron star, however infalling matter on neutron stars tends to build up in layers on the surface before igniting in sporadic thermonuclear explosions. These are not seen in black hole binaries.

Evidence for supermassive black holes at the centres of galaxies is also persuasive. In a fifteen year experiment from 1995 to 2009, Andrea Ghez and her colleagues at Caltech used stellar orbits to home in on an unseen 4 million solar mass object in a volume smaller than our solar system at the centre of the Milky Way. While a black hole would necessarily be much smaller even than this size, it is still the only theoretically plausible candidate. In the near future we hope to image the actual black hole event horizon at radio wavelengths (using the aptly named Event Horizon Telescope).

Other galactic centres are much further away, so we can't image them like we can the Milky Way. However, the Doppler shifts in spectroscopic images can tell us the range of speeds at which stars and gas clouds are moving, even without being able to image individual stars. The velocity dispersions for M87, a large galaxy in Virgo, indicate a black hole with a mass of 3 billion suns -- nearly a thousand times more massive than our Milky Way black hole. And indeed, the evidence is that most or all galaxies have supermassive black holes at their centres. Furthermore, the black hole mass seems to be proportional to the galaxy mass, for currently unknown reasons. We also have evidence of intermediate mass black holes (100 to 1 million solar masses) at the centre of the intermediate mass agglomerations of stars known as globular clusters.

Among the most exotic objects are the Active Galactic Nuclei (AGNs). These appear to be galactic centres which are being actively devoured by their central black holes. Stars and gas clouds falling into the black hole make them the most luminous objects in the universe. They can produce hundreds of times more energy in a year than our Sun will in its ten billion year lifetime. Yet it may be that the only difference between the AGNs and quiescent galactic centres like our own is that our black hole has temporarily stopped feeding. We might see fireworks in our home galaxy yet.

Of course, some of the strongest evidence of all for black holes has only been acquired in the last 18 months. The detection of gravitational waves by the LIGO observatory is consistent with two stellar mass black holes spiralling into each other and merging. The indications are that such events are relatively common in the universe.

And yet, there is a lot we don't know about black holes. How did supermassive black holes come to exist in the first place? Even the ones engaged in a feeding frenzy on a solar mass or two per year of infalling material would have difficulty getting to their current size by that mechanism alone. Could black holes have been initially formed during the Big Bang? Or have they grown from the bottom up, by successive mergers of galaxies and their respective black holes. The very large black hole in M87 is at the centre of an elliptical galaxy. Ellipticals are thought to form from mergers of spiral galaxies which are tidally disrupted as they coalesce. This is consistent with the bottom-up formation idea.

Eventually, we hope to detect supermassive black hole mergers using gravitational wave observatories. These waves would have much longer wavelengths than the ones detectable by LIGO. Instead they would need large space-based observatories like LISA, or would be based on pulsar timing by devices such as the new Chinese FAST radio telescope.

But it seems we may have evidence for such a merger even in advance of detecting the gravitational waves. It seems that if the spin axes of two black holes are appropriately aligned, and there is a large disparity of mass between the two, the merger of the black holes can produce anisotropic gravitational wave emission. This results in an asymmetrical kick whereby a portion of the gravitational wave energy delivers a large impetus to the resulting merged object. Obviously such an enormous object is difficult to get moving, so if we see one that appears to have been unseated from its position at the centre of the galaxy, and has a large velocity relative to the centre, we know something is up.

That's what has been discovered by Marco Chiaberge and others using the Hubble Space Telescope, and announced in a paper appearing today in Astronomy & Astrophysics*. The HST was used to image a quasar (an accreting supermassive black hole) called 3C 186. What the high resolution HST image has been able to show is that the quasar is not, in fact, at the centre of the galaxy but is offset by 1.3 seconds of arc from it, equating to 11 kiloparsecs or 35,000 light years distance. That's more than the distance of our Sun to the centre of our own galaxy.

Spectroscopy can be used to measure the speed of the black hole and its accretion disc relative to the surrounding gas. UV from Hubble's Faint Object Spectrograph and optical spectrographs from the Sloan Digital Sky survey were examined. (As an indicator of how much modern astronomy depends on archive data, the two spectrographs were taken in 1991 and 2000 respectively). It turns out that the black hole is speeding away from the galactic centre at over 2,000 kilometres per second. This should be above the escape velocity of the galaxy, so in about 20 million years the black hole will be marauding through intergalactic space. It'll take a lot longer for the lights to go out though, as the accretion disc is expected to last 100 million years before it is consumed. Working backward, the time since the supposed gravitational kick is about five million years.

The host galaxy also shows signs of "tidal tails" -- evidence of the disruption caused by a recent galaxy merger, and a further indication that the black hole itself formed from a merger. The galaxy cluster containing the host was discovered back in 2010 by Aneta Siemiginowska et al. using the Chandra X-Ray observatory, and was the most distant cluster containing an AGN known. A cluster is a more conducive environment for galaxy mergers.

The momentum of a supermassive black hole (estimated at 1 to 3 billion solar masses) fleeing the scene of an accident at such speed is difficult to explain by anything other than a gravitational kick. It would require the energy of a hundred million supernovas all delivering their energy in the same direction in concert, which is pretty much an impossibility. (Models suggest the biggest gravitational super-kicks could result in velocities of 5,000 km/s). Chiaberge et al do discuss three other interpretations of the data: i) the galaxy and the quasar are not connected at all but just superimposed in our line of sight, ii) the apparent velocity of the BH is actually the velocity of disc winds blowing off its accretion disc, iii) the BH velocity is the result of a slingshot from another AGN in the same galaxy rather than a gravitational wave kick. You'll have to read the paper to see why those possibilities are disfavoured.

A final point of interest is that 3C 186 is a radio loud AGN, a term which refers to strong radio emissions which often seem to originate from lobes of gas ejected in opposite direction from a galactic nucleus. Models suggest that RLAGNs may result from very rapidly spinning black holes, which again are more likely to be the result of a merger. Higher resolution imaging and spectroscopy, more detailed colour information, and longitudinal accretion disk observations may be carried out in future to further nail down the properties of 3C 186.

* M. Chiaberge et al., "The puzzling case of the radio-loud QSO 3C 186: a gravitational wave recoiling black hole in a young radio source?", A & A, March 2017. Available online here.


Two papers for the price of one, bonus factoid:

If you were bored/nerdy/nuts enough to follow all the links you'll have seen a surprise result in the Andrea Ghez video that some of the stars orbiting the Milky Way SMBH are unexpectedly young. While this is still unexplained, it turns out that new stars can be formed in the outflows from AGNs at fast rates of a dozen solar masses per year. Ram pressure in the outflow compresses gas and triggers star formation, with the resulting stars then following ballistic trajectories and arcing back down into the central galaxy bulge. Published this week in Nature, Maiolino et al., "Star formation inside a galactic outflow", online here, preprint here, youtube here.

Gwynston

Fascinating read!

I wonder if it isn't time to come up with a better name for black holes? That name, and the way they've been portrayed in SciFi over the years, conjures up the idea of mysterious "holes" in the fabric of space that pull things inexorably inwards to their destruction (or perhaps through a wormhole to somewhere else )

But in fact all they are, are incredibly massive, dense "things" with so much gravity, even light is pulled in. So we can't directly image them with light, but in other ways can't they be thought of as similar to other stellar objects in their formation, accretion and interaction with their surroundings - just that they're way more massive?

Or am I over-simplifying things?

Whatever - I don't think they should be called "holes". Any suggestions for a better name? I've heard that the Russian name translates as "frozen star" and another suggestion I've heard is "collapsar".

Gwynston

I guess what I'm trying to say is - they're not really holes. There's an object there, even if it is hard to conceptualize how so much matter can be contained in such a small space.

Which begs the question - what's it actually like in there?
Is it all the atoms (and subatomic particles) from the accreted matter squashed together as close as they can get? (I know generally there is mostly space in a regular atom, so there's a lot of room for compression.)

But how close together is everything? Are all the particles with mass physically squashed up against each other with no space in between? e.g. does the huge gravity override any charge repulsion between particles?

I'm aware that they have a certain size which is respective to their mass, so that suggests that everything is squished as much as it can be and adding more matter inevitably adds size?

RebelButtMunch

I thought the current thinking was that there was a singularity inside with infinite density etc. I never really believed that because I don't think infinity exists in the physical world.

Gwynston

I think the singularity is a theoretical concept for certain masses.
But large black holes do have a physical size, as I understand it.

There are plenty of references to black holes with a mass of x million solar masses fitting in a space the size of the Earth (or whatever...)

ps200306

Gwynston wrote: »

But in fact all they are, are incredibly massive, dense "things" with so much gravity, even light is pulled in. So we can't directly image them with light, but in other ways can't they be thought of as similar to other stellar objects in their formation, accretion and interaction with their surroundings - just that they're way more massive?

Or am I over-simplifying things?

Whatever - I don't think they should be called "holes". Any suggestions for a better name? I've heard that the Russian name translates as "frozen star" and another suggestion I've heard is "collapsar".

Gwynston wrote: »

I guess what I'm trying to say is - they're not really holes. There's an object there, even if it is hard to conceptualize how so much matter can be contained in such a small space.

Yes, I think it's a bit more complicated than that. I'll take a stab at a few of your questions, before returning to the concept of "frozen stars".

Gwynston wrote: »

Which begs the question - what's it actually like in there?
Is it all the atoms (and subatomic particles) from the accreted matter squashed together as close as they can get? (I know generally there is mostly space in a regular atom, so there's a lot of room for compression.)

That is actually a pretty good description of a neutron star, but not of a black hole. Normal matter refuses to be compressed beyond a certain point because electrons cannot be squeezed together into an arbitrarily small space. The Heisenberg Uncertainty Principle sets the size of a neutral hydrogen atom -- it is the smallest volume within which a bound electron can be localised, even though that volume is a thousand trillion times the volume of the much tinier nucleus (hence all the empty space you mentioned). The Pauli Exclusion Principle prohibits more than two electrons from occupying that smallest volume. (The underlying reason for this takes us deep into the realm of quantum mechanics -- see here and here for a bit more info).

Our Sun's core has more than a dozen times the density of lead, but the average separation between atomic nuclei is still five times the diameter of a neutral hydrogen atom. So there is plenty of space for electrons to hide, even though stripped from their atoms by high temperature. Collisions between particles in the solar core are still elastic so that the plasma behaves broadly like an ideal gas, expanding and contracting adiabatically in response to temperature changes and thus automatically balancing the opposing forces of gravity and radiation pressure.

When the pressure rises beyond a certain limit, it is like the bottoming out of a car's suspension. (When you go over a speed bump, the force exerted by your suspension is proportional to the distance by which the supension is compressed, but when it bottoms out you hit a hard limit). When a star's core contracts sufficiently the pressure is no longer due to elastic collisions, but to the Pauli Exclusion Principle, a condition called electron degeneracy. In some stars, this is as far as things can go. Our own star will end up as a white dwarf, which is the remaining core still held up by electron degeneracy pressure after it has heated and jettisoned its outer layers. From here on it will slowly cool over countless trillions of years.

In more massive stars, the exhaustion of fuel and continued gravitational collapse results in pressures higher than can be supported by electron degeneracy. In such cases, electrons can no longer exist and are forced to combine with protons to form neutrons in a process called inverse beta decay. That's how neutron stars are formed. Now, neutrons -- like electrons and protons -- are still fermions. They obey the same Pauli Exclusion Principle as all fermions, but their much greater mass allows them to be localised to a much smaller volume. (The Heisenberg uncertainty in position is inversely proportional to mass).

A white dwarf is a hundred thousand times denser than lead, and a neutron star is a million times denser than a white dwarf, but it is still prevented from forming a black hole by neutron degeneracy pressure.

Gwynston wrote: »

But how close together is everything? Are all the particles with mass physically squashed up against each other with no space in between? e.g. does the huge gravity override any charge repulsion between particles?

Just as electrons cannot exist when electron degeneracy is overwhelmed by gravity, neutrons cannot exist when a black hole forms. Even hypothetical quark degenerate material cannot exist. We don't know exactly what form it takes, but the matter must be converted into some sort of boson, i.e. non-fermionic material which does not obey the Pauli Exclusion Principle. The bosons are particles with a different type of spin to fermions, and they include photons among others. Not all bosons are neutral, but conservation of charge does not rule out the production of neutral bosons since the neutrons had no net charge, just like the quasi-neutral plasma from which they formed.

Gwynston wrote: »

I'm aware that they have a certain size which is respective to their mass, so that suggests that everything is squished as much as it can be and adding more matter inevitably adds size?

RebelButtMunch wrote: »

I thought the current thinking was that there was a singularity inside with infinite density etc. I never really believed that because I don't think infinity exists in the physical world.

Gwynston wrote: »

I think the singularity is a theoretical concept for certain masses.
But large black holes do have a physical size, as I understand it.

There are plenty of references to black holes with a mass of x million solar masses fitting in a space the size of the Earth (or whatever...)

We have to be super-careful with our terminology here, because you may both be correct. When people refer to the "size" of a black hole they are not referring to a physical object. They are talking about the extent of the event horizon, a non-physical boundary at which the escape velocity exceeds the speed of light. Remember, the escape velocity is an age-old Newtonian definition. It's the speed at which an object at a given distance from a gravitating body must travel away from it in order to never be pulled back in. It's given by:



where M is the mass of the body, r the distance from it, and G is the universal gravitational constant. (This formula can be very easily derived from Newton's equation for the force of gravity). So if we want to know the so-called Schwarzschild distance at which the escape velocity exceeds the speed of light we just replace with the speed of light c, and rearrange to get r:



A black hole is any object which is smaller than its Schwarzschild radius. Beyond that we don't need to know what size it actually is, and it turns out we can't know. This is for reasons to do with Einstein's General Theory of Relativity. One of the results from General Relativity is that time slows down in the vicinity of a gravitating body from the point of view of an observer further away. For example, an observer aloft in a hot air balloon will see his clock run faster than one that he sees through his binoculars down at ground level, but the difference is very tiny for a body like the Earth.

The general formula for the rate at which time runs at a distance r from a gravitating body from the point of view of an observer far away is:



where is the rate of passage of time at distance r, and is the rate for the distant observer. At the Schwarzschild radius, we would then have:



In other words, a distant observer sees time stand still at the event horizon of a black hole. This is where the notion of a "frozen star" comes from. Imagine you could watch a star's core undergo gravitational collapse to form a black hole. As the radius of the star decreases, gravitational time dilation causes the passage of time to slow. This affects all physical processes; for instance, the time between successive cycles of light waves increases so that the frequency is lower and the light gets redder. As the star reaches the Schwarzschild radius time stops altogether! The surface -- if we could see it -- would be frozen in mid-collapse. But we can't see it because light can no longer escape, and even if it could it would be infinitely red-shifted.

Now, we must remember that this is all from the perspective of a distant observer outside the event horizon. Unfortunately we have to wrap our head around the difficult concept that two observers can see time flowing at different rates for the same events. An observer falling with the star as it collapsed would experience the passage of time as normal. But even if he survived, once he passed inside the event horizon he could never report back to us what was going on inside. Does the star reach a singularity of infinite density and infinitesimal size? We have no physics to describe such a thing, but the short answer is we simply don't know. And in our region of the universe outside the event horizon it doesn't really matter because the black hole is frozen at the event horizon infinitely far into our future.

Gwynston

Wow PS - thanks for such a comprehensive reply!
You have a great way of making these complex subjects understandable to the layman. (Or at least to me - I did A-level Physics and some degree-level Chemistry, so my knowledge of Standard Model particles is limited and my exposure to astrophysics is purely from high level-reading).

Your description left almost nothing unresolved in my mind, but this did stoke a new question in me:

ps200306 wrote: »

Does the star reach a singularity of infinite density and infinitesimal size? We have no physics to describe such a thing, but the short answer is we simply don't know. And in our region of the universe outside the event horizon it doesn't really matter because the black hole is frozen at the event horizon infinitely far into our future.

So from our perspective of time's passing, will all the black holes in the universe stay the same to us? And since black holes will continue to form, will the universe we see just fill up with black holes which we are destined to be frozen forever?

Or is it just the "black" part beyond the event horizon which we are destined to never be able to see any of? e.g. could the space around where we know black holes are gradually fill the "gap" as a black hole degenerates? (through Hawking Radiation?)

ps200306

The event horizon of a black hole expands as it accretes matter or merge with other black holes. Although time is frozen at the event horizon from our perspective, there is nothing to stop the event horizon expanding in a finite time. (Remember it is just a non-physical boundary).

Yes, black holes will continue to form. Obviously the number of them must be finite, since they must form either from stars or from mergers of existing black holes, and the observable region of the universe is finite. As the universe expands, the observable part of it becomes more and more empty, so in the very far future we won't be able to see much of anything at all. The existing black holes will eventually evaporate through Hawking radiation, but the observable universe will be very empty by that time since the evaporation time for a supermassive black hole is on the order of years.

And that's ignoring that the temperature of a large black hole is much smaller than the current Cosmic Microwave Background temperature, so in fact black holes absorb more CMB photons than they emit Hawking radiation photons, and thus won't even start evaporating until after the universe cools to below their temperature. For an SMBH that will not be until the universe is a million times its current age. As a result, we can pretty much ignore Hawking radiation for all practical purposes.

ThunderCat

ps200306 wrote: »

Yes, I think it's a bit more complicated than that. I'll take a stab at a few of your questions, before returning to the concept of "frozen stars".




That is actually a pretty good description of a neutron star, but not of a black hole. Normal matter refuses to be compressed beyond a certain point because electrons cannot be squeezed together into an arbitrarily small space. The Heisenberg Uncertainty Principle sets the size of a neutral hydrogen atom -- it is the smallest volume within which a bound electron can be localised, even though that volume is a thousand trillion times the volume of the much tinier nucleus (hence all the empty space you mentioned). The Pauli Exclusion Principle prohibits more than two electrons from occupying that smallest volume. (The underlying reason for this takes us deep into the realm of quantum mechanics -- see here and here for a bit more info).

Our Sun's core has more than a dozen times the density of lead, but the average separation between atomic nuclei is still five times the diameter of a neutral hydrogen atom. So there is plenty of space for electrons to hide, even though stripped from their atoms by high temperature. Collisions between particles in the solar core are still elastic so that the plasma behaves broadly like an ideal gas, expanding and contracting adiabatically in response to temperature changes and thus automatically balancing the opposing forces of gravity and radiation pressure.

When the pressure rises beyond a certain limit, it is like the bottoming out of a car's suspension. (When you go over a speed bump, the force exerted by your suspension is proportional to the distance by which the supension is compressed, but when it bottoms out you hit a hard limit). When a star's core contracts sufficiently the pressure is no longer due to elastic collisions, but to the Pauli Exclusion Principle, a condition called electron degeneracy. In some stars, this is as far as things can go. Our own star will end up as a white dwarf, which is the remaining core still held up by electron degeneracy pressure after it has heated and jettisoned its outer layers. From here on it will slowly cool over countless trillions of years.

In more massive stars, the exhaustion of fuel and continued gravitational collapse results in pressures higher than can be supported by electron degeneracy. In such cases, electrons can no longer exist and are forced to combine with protons to form neutrons in a process called inverse beta decay. That's how neutron stars are formed. Now, neutrons -- like electrons and protons -- are still fermions. They obey the same Pauli Exclusion Principle as all fermions, but their much greater mass allows them to be localised to a much smaller volume. (The Heisenberg uncertainty in position is inversely proportional to mass).

A white dwarf is a hundred thousand times denser than lead, and a neutron star is a million times denser than a white dwarf, but it is still prevented from forming a black hole by neutron degeneracy pressure.




Just as electrons cannot exist when electron degeneracy is overwhelmed by gravity, neutrons cannot exist when a black hole forms. Even hypothetical quark degenerate material cannot exist. We don't know exactly what form it takes, but the matter must be converted into some sort of boson, i.e. non-fermionic material which does not obey the Pauli Exclusion Principle. The bosons are particles with a different type of spin to fermions, and they include photons among others. Not all bosons are neutral, but conservation of charge does not rule out the production of neutral bosons since the neutrons had no net charge, just like the quasi-neutral plasma from which they formed.






We have to be super-careful with our terminology here, because you may both be correct. When people refer to the "size" of a black hole they are not referring to a physical object. They are talking about the extent of the event horizon, a non-physical boundary at which the escape velocity exceeds the speed of light. Remember, the escape velocity is an age-old Newtonian definition. It's the speed at which an object at a given distance from a gravitating body must travel away from it in order to never be pulled back in. It's given by:



where M is the mass of the body, r the distance from it, and G is the universal gravitational constant. (This formula can be very easily derived from Newton's equation for the force of gravity). So if we want to know the so-called Schwarzschild distance at which the escape velocity exceeds the speed of light we just replace with the speed of light c, and rearrange to get r:



A black hole is any object which is smaller than its Schwarzschild radius. Beyond that we don't need to know what size it actually is, and it turns out we can't know. This is for reasons to do with Einstein's General Theory of Relativity. One of the results from General Relativity is that time slows down in the vicinity of a gravitating body from the point of view of an observer further away. For example, an observer aloft in a hot air balloon will see his clock run faster than one that he sees through his binoculars down at ground level, but the difference is very tiny for a body like the Earth.

The general formula for the rate at which time runs at a distance r from a gravitating body from the point of view of an observer far away is:



where is the rate of passage of time at distance r, and is the rate for the distant observer. At the Schwarzschild radius, we would then have:



In other words, a distant observer sees time stand still at the event horizon of a black hole. This is where the notion of a "frozen star" comes from. Imagine you could watch a star's core undergo gravitational collapse to form a black hole. As the radius of the star decreases, gravitational time dilation causes the passage of time to slow. This affects all physical processes; for instance, the time between successive cycles of light waves increases so that the frequency is lower and the light gets redder. As the star reaches the Schwarzschild radius time stops altogether! The surface -- if we could see it -- would be frozen in mid-collapse. But we can't see it because light can no longer escape, and even if it could it would be infinitely red-shifted.

Now, we must remember that this is all from the perspective of a distant observer outside the event horizon. Unfortunately we have to wrap our head around the difficult concept that two observers can see time flowing at different rates for the same events. An observer falling with the star as it collapsed would experience the passage of time as normal. But even if he survived, once he passed inside the event horizon he could never report back to us what was going on inside. Does the star reach a singularity of infinite density and infinitesimal size? We have no physics to describe such a thing, but the short answer is we simply don't know. And in our region of the universe outside the event horizon it doesn't really matter because the black hole is frozen at the event horizon infinitely far into our future.

Fantastic post ps200306, I was entranced reading it. Great stuff.

ps200306

ThunderCat wrote: »

Fantastic post ps200306, I was entranced reading it. Great stuff.

Gwynston wrote: »

Wow PS - thanks for such a comprehensive reply! You have a great way of making these complex subjects understandable to the layman.

I'm just a layman struggling to understand them myself

mickmackey1

Is Hawking radiation a proven fact?? I was under the impression it's just a theory, which is why the bould Stevie is still waiting for his Nobel.

ps200306

mickmackey1 wrote: »

Is Hawking radiation a proven fact?? I was under the impression it's just a theory, which is why the bould Stevie is still waiting for his Nobel.

It certainly isn't an observational fact. None of the astrophysical black holes we know about (i.e. stellar mass and upward) could produce any detectable Hawking radiation. Only relatively tiny black holes would have a detectable temperature so we would be relying on nearby primordial micro black holes or manufacturing our own at CERN or somesuch -- neither of which is in the realm of understood theory or practice.

Nevertheless, if black holes are truly non-radiating, it would imply a temperature of absolute zero at the event horizon, a condition that is forbidden by the Uncertainty Principle. So we do have reasons to suspect that black holes radiate even if the precise mechanism is not known.