<p>The paper says</p>
<blockquote>
<p>At the onset of shell expansion, there are two energy reservoirs: the input energy of the quasar itself, <span class="math-container">$E_0$</span>, and the kinetic energy of the preexisting Hubble flow within a distance <span class="math-container">$R_\text{max}$</span> of the quasar, <span class="math-container">$(3/10)M_s v^2$</span>.</p>
</blockquote>
<p>The latter is the Newtonian kinetic energy of uniformly distributed, uniformly expanding dust:</p>
<p><span class="math-container">$$\int \frac12 v^2 dm = \int_0^{R_\text{max}} \frac12 (Hr)^2 (4πr^2ρ\,dr) = \frac25 π ρ H^2 R_\text{max}^5 = \frac3{10}M_s v^2$$</span></p>
<p>where <span class="math-container">$M_s = \frac43 π R_\text{max}^3 ρ$</span> and <span class="math-container">$v = H R_\text{max}$</span>.</p>
<p>A fraction <span class="math-container">$f_d$</span> of that, plus the energy <span class="math-container">$E_0$</span> of the explosion, is supposed to equal the kinetic energy of the final thin-shell state, <span class="math-container">$\frac12 M_s v^2$</span>.</p>
<p>It's not clear to me that this model makes sense, since the distances involved (~1 Mpc comoving) seem too small for uniform Hubble expansion to be a good approximation even at <span class="math-container">$z=10$</span>. But in any case, the extra energy in the model comes from the motion of surrounding matter, and not from a cosmological expansion force.</p>

CC BY-SA 4.0
2022-12-02T10:54:41.420Z
but wouldn't the extra energy from the motion of surrounding matter come from the Hubble flow one way or another after all? @benrg
vengaq
CC BY-SA 4.0
2022-12-02T19:04:57.330Z
@vengaq Yes, it's energy of the Hubble flow. I think my answer was influenced by your other questions about extracting unlimited energy from cosmological expansion; I wanted to make the point that this is kinetic energy left over from the big bang, not energy being added on an ongoing basis by an expansion force.
benrg
CC BY-SA 4.0
2022-12-04T20:38:09.040Z
and even if you have doubts about the validity of the model, has there been any observations in similar conditions where the Hubble flow would indeed "inject" some energy in a similar situation? @benrg
vengaq
CC BY-SA 4.0
2022-12-05T20:54:36.167Z
@vengaq I don't know what's been seen experimentally. I should probably clarify that there's nothing unreasonable about nearby matter being caught up in the explosion and contributing kinetic energy to it. I was only suspicious of how uniform they assumed the nearby matter to be.
benrg
CC BY-SA 4.0
2022-12-01T05:36:06.400Z
2022-12-01T05:36:06.400Z
benrg
<p>I found <a href="https://iopscience.iop.org/article/10.1086/321630" rel="nofollow noreferrer">this article</a> about the behavior of quasar outflows in cosmology and how they can create a magnetic field.</p>
<p>In section 2.1.4., the authors say that when a quasar produces a &quot;wave&quot; 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.</p>
<p>Does this really mean that the expansion of the universe can inject energy into these outflows? Are there any other papers acknowledging this?</p>
<p>Then, is energy conserved in this case? Wouldn't the Hubble expansion be adding &quot;new&quot; energy to the system according to the article?</p>

<cosmology><magnetic-field><galactic-dynamics><quasars><active-galaxy>
Can the Hubble expansion inject energy in AGN and quasar outflows?
vengaq
# Can the Hubble expansion inject energy in AGN and quasar outflows?

(Asked by: username_0 on 2022-11-30)

I found [this article](https://iopscience.iop.org/article/10.1086/321630) 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.

Does this really mean that the expansion of the universe can inject energy into these outflows? Are there any other papers acknowledging this?

Then, is energy conserved in this case? Wouldn't the Hubble expansion be adding "new" energy to the system according to the article?

**Tags:** cosmology, magnetic-field, galactic-dynamics, quasars, active-galaxy


---

## 1 answers

### Answer by username_1 on 2022-12-01. Score: 1

The paper says

> At the onset of shell expansion, there are two energy reservoirs: the input energy of the quasar itself, $E\_0$, and the kinetic energy of the preexisting Hubble flow within a distance $R\_\text{max}$ of the quasar, $(3/10)M\_s v^2$.

The latter is the Newtonian kinetic energy of uniformly distributed, uniformly expanding dust:

$$\int \frac12 v^2 dm = \int\_0^{R\_\text{max}} \frac12 (Hr)^2 (4πr^2ρ\,dr) = \frac25 π ρ H^2 R\_\text{max}^5 = \frac3{10}M\_s v^2$$

where $M\_s = \frac43 π R\_\text{max}^3 ρ$ and $v = H R\_\text{max}$.

A fraction $f\_d$ of that, plus the energy $E\_0$ of the explosion, is supposed to equal the kinetic energy of the final thin-shell state, $\frac12 M\_s v^2$.

It's not clear to me that this model makes sense, since the distances involved (~1 Mpc comoving) seem too small for uniform Hubble expansion to be a good approximation even at $z=10$. But in any case, the extra energy in the model comes from the motion of surrounding matter, and not from a cosmological expansion force.

> **Comments:**
> **username_0**: but wouldn't the extra energy from the motion of surrounding matter come from the Hubble flow one way or another after all? @username_1  
> **username_1**: @username_0 Yes, it's energy of the Hubble flow. I think my answer was influenced by your other questions about extracting unlimited energy from cosmological expansion; I wanted to make the point that this is kinetic energy left over from the big bang, not energy being added on an ongoing basis by an expansion force.  
> **username_0**: and even if you have doubts about the validity of the model, has there been any observations in similar conditions where the Hubble flow would indeed "inject" some energy in a similar situation? @username_1  
> **username_1**: @username_0 I don't know what's been seen experimentally. I should probably clarify that there's nothing unreasonable about nearby matter being caught up in the explosion and contributing kinetic energy to it. I was only suspicious of how uniform they assumed the nearby matter to be.  

---

