Conservation of energy in quasar outflows?

[Suekdccia]

TL;DR Summary

Conservation of energy in quasar outflows?

I found this article* about the behavior of quasar outflows in cosmology and how they can create a magnetic field.

In section 2.1.4., the authors say that when a quasar produces a "wave" or an outflow, the material will be emitted with energy coming from both the quasar itself and the Hubble flow of the expansion of the Universe itself.

Then, is energy conserved in this case? Wouldn't the Hubble expansion be adding "new" energy to the system?* https://iopscience.iop.org/article/10.1086/321630

 

[kimbyd]

My reading of it is that they're saying there are two reservoirs of energy: the input energy of the quasar, and the kinetic energy of the matter that makes up the Hubble flow. To do this, they're operating in a coordinate system that is not moving with the expansion (the amount of energy depends upon your coordinate system, but the physics should work out the same either way).

Then they're applying an adiabatic assumption to the system, and saying energy must be conserved in this coordinate system. Energy is not conserved in general, and in particular isn't conserved in an expanding universe. But energy is conserved in a flat coordinate system for an expanding universe, so this tracks.

 

[Suekdccia]

My reading of it is that they're saying there are two reservoirs of energy: the input energy of the quasar, and the kinetic energy of the matter that makes up the Hubble flow. To do this, they're operating in a coordinate system that is not moving with the expansion (the amount of energy depends upon your coordinate system, but the physics should work out the same either way).

Then they're applying an adiabatic assumption to the system, and saying energy must be conserved in this coordinate system. Energy is not conserved in general, and in particular isn't conserved in an expanding universe. But energy is conserved in a flat coordinate system for an expanding universe, so this tracks.

But there is something I do not understand:

As you say, although energy is not conserved in general at cosmological scales, it is conserved in local systems (like inside our galaxy or our solar system). However in local systems the Hubble expansion is not taken into account as it has no effects in local scales (as gravity dominates). However, in the authors' system, they consider the energy that the Hubble expansion gives to their system. So, in this case, how is energy conserved, if we are adding an extra input of energy (given by the Hubble expansion)?

 

[kimbyd]

But there is something I do not understand:

As you say, although energy is not conserved in general at cosmological scales, it is conserved in local systems (like inside our galaxy or our solar system). However in local systems the Hubble expansion is not taken into account as it has no effects in local scales (as gravity dominates). However, in the authors' system, they consider the energy that the Hubble expansion gives to their system. So, in this case, how is energy conserved, if we are adding an extra input of energy (given by the Hubble expansion)?

General Relativity conserves the stress-energy tensor. This is a quantity that contains energy, momentum, pressure, and shear forces. This conservation law can be reduced to energy conservation in specific circumstances. In this case they're implicitly considering a fixed coordinate system (i.e., one that doesn't change with time). That lack of change in time forces energy conservation.

One way that you can see that this works is to consider a [ire;u Newtonian universe. In this universe, we're using simple Newtonian physics to describe the expansion, which requires the assumption that we're working with just matter (no dark energy, no radiation, but dark matter is fine). We're also taking a finite-volume sphere of said universe out to some distance.

This universe, which uses Newtonian physics only, perfectly reproduces the Friedmann equations which we get from the full General Relativity view of the expanding universe, as long as we are only talking about the special case of matter domination. Now, in this view, would you agree that energy must be conserved in such a universe? After all, it follows Newtonian physics, and energy is conserved in Newtonian physics. And in this Newtonian view, the energy of the system will be made up of a combination of kinetic energy from the outflow of matter from the center, and gravitational potential energy.

Something analogous happens when you consider General Relativity, but consider a local region using fixed coordinates (i.e., coordinates which do not grow with the expansion). Within that local region, energy will be conserved. And this "local region" can be pretty big before the math starts to break down (I believe it can't stretch out as far as any horizons, but anything short of that should be fair game).

Anyway, I can't say for sure that they did everything right in this paper, as I don't understand the details of the paper. But at least on its face it's not absurd to think of energy in an expanding universe in this way.

 

[Suekdccia]

Galactic winds (or outflows) are produced by AGNs, quasars, super novas...etc which basically eject matter usually in form of waves or spheres, sometimes even arriving to the IGM (Intergalactic Medium) composed by gas (which, when "at rest", it moves along the Hubble flow).

Having said this, does the matter moving with the Hubble flow influence the energy content of these galactic winds? Does it add more kinetic energy to it (as this paper [1] seems to mention: see section 2.3)?

[1]: https://reu.physics.ucla.edu/common/papers/2011/benjamin_sarah.pdf