10

In the book The Cosmic Perspective, it is stated that as matter is falling into a supermassive black hole, up to $40\%$ of its mass are converted to thermal energy, making the accretion of matter around a black hole a vastly more efficient energy source than even fusion. But what is the mechanism behind this conversion of mass to thermal energy?

uhoh
  • 31,151
  • 9
  • 89
  • 293
Vercassivelaunos
  • 203
  • 6

2 Answers2

21

The "mass" falling in is the rest mass (at infinity). As the matter falls it gains kinetic energy. Most of the matter cannot fall directly into the black hole because it encounters a potential barrier due to its angular momentum with respect to the black hole, so it enters some sort of orbit. The orbiting matter accumulates in an accretion disk.

To fall into the black hole, the matter must lose angular momentum. It does this via friction. At a microscopic level, interactions between particles and possibly with magnetic fields, transfer angular momentum outwards and also heat the disk material. The hot disk effectively radiates away (some of) the kinetic energy that the matter gained by falling towards the black hole and the matter moves inwards, eventually falling into the black hole. This radiated energy can be a significant fraction of the rest mass energy of the matter because it is moving relativistically when it gets close to the black hole.

One way of looking at the whole process is in terms of conservation of mass/energy. The start point is the black hole plus the rest mass energy of the material that is to be accreted. After accretion the black hole has accreted some of that mass-energy, but a fraction of it has been radiated away as it passes through the accretion disk. Thus, as @Sten points out, the mass accreted by the black hole is less than the rest mass that fell into it - the difference emerges as radiation.

ProfRob
  • 151,483
  • 9
  • 359
  • 566
  • So the mass that is converted to heat is really the mass of the black-hole-accretion-disc system? Would that be a valid way to look at it? – Vercassivelaunos Jun 18 '23 at 13:09
  • 5
    @Vercassivelaunos The "mass" that is converted is "relativistic mass", which is an outdated concept. The rest mass remains unchanged. – David Hammen Jun 18 '23 at 13:44
  • 2
    @DavidHammen The invariant mass of the black hole-accretion disk system does drop (and the invariant mass of a composite system is not an outdated concept). – Sten Jun 19 '23 at 06:49
  • 2
    Another perspective is that the mass gained by the black hole is smaller than the summed rest masses of the accreted particles. – Sten Jun 19 '23 at 06:52
  • @DavidHammen The death of relativistic mass as a concept is vastly exaggerated. And it is the easiest concept here. – John Doty Jun 20 '23 at 22:16
  • The mechanism of the friction isn't well understood, but is widely thought to involve magnetic turbulence in the rotating plasma. – John Doty Jun 20 '23 at 22:20
  • @JohnDoty no it's not the easiest. The use of relativistic mass here is quite confusing in fact (to me). From the description it seems that what's actually meant is that the kinetic energy that was gained during the fall is partially shed by radiation, and this is how the total mass of the BH+accretion disk gets reduced. – Ruslan Jun 21 '23 at 10:26
  • @Ruslan Mass that's conserved is much easier to reason about in problems like this than mass that disappears. Best to master both approaches. But that's unfashionable. – John Doty Jun 21 '23 at 12:48
  • Things are more complicated by the fact that significant fractions of the gas in the accretion disc will never end in the hole, but be blown away as a wind. – Walter Jun 28 '23 at 22:47
3

All else being equal, the same object will produce less far-field gravitational force, the deeper it is in a gravitational well. This is not intuitive if you are used to newtonian gravity, but it’s the same principle as a helium atom weighing less than two deuterium atoms.

If gas is dropped straight into a black hole, this reduction is exactly cancelled out by the increase in far field gravitational pull caused by the increase in kinetic energy of the gas. If the gas is slowed down on the way down, then the effects don’t cancel.

QuadmasterXLII
  • 131
  • 2