<p>Here is a study from 2012 for the largest recorded quasar which quotes an output of 400 times the mass of the sun per year, which is 253 earth masses per minute (133178400 M ⊕ / 525600 mins) at 2.5 percent the speed of light, located 1 billion light years away.</p>

<p><a href="https://vtnews.vt.edu/articles/2012/11/112912-science-quasar.html" rel="nofollow noreferrer">https://vtnews.vt.edu/articles/2012/11/112912-science-quasar.html</a></p>

<p>It's the largest recorded quasar, I don't know the figure for the largest theoretical quasar, there are apparently <a href="http://www.dailygalaxy.com/my_weblog/2012/11/monster-quasar-discovered-with-power-outflow-100-times-milky-way-galaxy.html" rel="nofollow noreferrer">hundreds of people</a> theorizing and debating the theoretical maximum.</p>

<p><a href="https://i.sstatic.net/t2wst.jpg" rel="nofollow noreferrer" title="SDSS J1106+1939"><img src="https://i.sstatic.net/t2wst.jpg" alt="SDSS J1106+1939" title="SDSS J1106+1939"></a></p>

CC BY-SA 4.0
2018-07-06T07:21:15.417Z
The question asks about the mass accretion rate, not the size of any outflow.
ProfRob
CC BY-SA 4.0
2018-07-04T06:45:46.013Z
2018-07-06T04:12:54.213Z
2018-07-06T04:12:54.213Z
bandybabboon
<p>Tricky to say for sure, but I would imagine it comes about from measurements of the luminosity and inference of the black hole mass in such systems.</p>

<p>The most extreme objects radiate at the <a href="https://en.wikipedia.org/wiki/Eddington_luminosity" rel="noreferrer">Eddington luminosity</a>, where gravitational forces on matter falling into the black hole are balanced by radiation pressure from the heated material closer in.</p>

<p>If infalling mass is converted to luminosity at a rate of 
$$ L = \epsilon \dot{M} c^2,$$
where $\dot{M}$ is the mass accretion rate, $L$ is the luminosity and $\epsilon$ is an efficiency factor, which should be of order 0.1; then the mass accretion rate at the Eddington limit is given by
$$ \dot{M} = \frac{4\pi G M m_p}{\epsilon c \sigma_T} \simeq 1.4\times 10^{15}\frac{M}{M_{\odot}}\ {\rm kg/s},$$
where $M$ is the black hole mass, $m_p$ the mass of a proton and $\sigma_T$ is the Thomson scattering cross-section for free electrons (the major source of opacity in the infalling hot gas).</p>

<p>The biggest supermassive black holes in the universe have $M \simeq 10^{10}M_{\odot}$ and thus the Eddington accretion rate for such objects is about $1.4\times 10^{25}$ kg/s or about 2.3 Earths/second or 140 Earths per minute. The difference between this estimate and the one on the wikipedia page could be what is assumed for the biggest $M$ or that $\epsilon$ is a bit smaller than 0.1 or indeed that the luminosity could exceed the Eddington luminosity (because the accretion isn't spherical).</p>

<p>Perhaps a simpler way to get the answer is to find the most luminous quasar and divide by $\epsilon c^2$. The most luminous quasar ever seen is probably something like <a href="http://www.mdpi.com/2075-4434/5/1/3/pdf" rel="noreferrer">3C 454.3</a>, which reaches $\sim 5\times 10^{40}$ Watts in its highest state. Using $\epsilon = 0.1$ yields about an Earth mass per second for the accretion rate.</p>

<p>So perhaps the number on the wikipedia page is a <em>little</em> exaggerated.</p>

CC BY-SA 4.0
2018-07-04T02:29:47.533Z
Great answer! Your link to 3C 454.3 (http://www.mdpi.com/2075-4434/5/1/3/pdf) doesn't work. 
EDIT: Just found a chached copy at
http://webcache.googleusercontent.com/search?q=cache:iafbgurch_wJ:www.mdpi.com/2075-4434/5/1/3/pdf+&cd=12&hl=en&ct=clnk&gl=nz
Jim421616
CC BY-SA 4.0
2018-07-04T03:33:34.993Z
Using your equation for M-dot, and the mass of 3C273 of 886 million solar masses I get 1.24E18 kg/s. Does that sound right? For the Thomson scattering cross-section I used 6.65E-29 m^2
Jim421616
CC BY-SA 4.0
2018-07-04T03:47:47.450Z
@Jim421616 No, you forgot the factor of a million!
ProfRob
CC BY-SA 4.0
2018-07-04T03:51:02.467Z
Oh yes, I just saw that I used the wrong mass for solar :)
Jim421616
CC BY-SA 4.0
2018-07-03T23:27:33.210Z
2018-07-03T23:38:29.803Z
2018-07-03T23:38:29.803Z
ProfRob
<p>This page on <a href="https://en.wikipedia.org/wiki/Quasar" rel="noreferrer">Wikipedia -- Quasars</a> mentions that the "The largest known [quasar] is estimated to consume matter equivalent to 600 Earths per minute". However, there is no citation for this comment. How can I find out where this information came from? I've commented in the <a href="https://en.wikipedia.org/wiki/Talk:Quasar" rel="noreferrer">Talk</a> section for the page.</p>

<quasars><accretion-discs>
Quasar mass and accretion rates
Jim421616
# Quasar mass and accretion rates

(Asked by: username_0 on 2018-07-03)

This page on [Wikipedia -- Quasars](https://en.wikipedia.org/wiki/Quasar) mentions that the "The largest known [quasar] is estimated to consume matter equivalent to 600 Earths per minute". However, there is no citation for this comment. How can I find out where this information came from? I've commented in the [Talk](https://en.wikipedia.org/wiki/Talk:Quasar) section for the page.

**Tags:** quasars, accretion-discs

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## 2 answers

### Answer by username_2 on 2018-07-03. Score: 12 | Accepted answer

Tricky to say for sure, but I would imagine it comes about from measurements of the luminosity and inference of the black hole mass in such systems.

The most extreme objects radiate at the [Eddington luminosity](https://en.wikipedia.org/wiki/Eddington_luminosity), where gravitational forces on matter falling into the black hole are balanced by radiation pressure from the heated material closer in.

If infalling mass is converted to luminosity at a rate of
$$ L = \epsilon \dot{M} c^2,$$
where $\dot{M}$ is the mass accretion rate, $L$ is the luminosity and $\epsilon$ is an efficiency factor, which should be of order 0.1; then the mass accretion rate at the Eddington limit is given by
$$ \dot{M} = \frac{4\pi G M m\_p}{\epsilon c \sigma\_T} \simeq 1.4\times 10^{15}\frac{M}{M\_{\odot}}\ {\rm kg/s},$$
where $M$ is the black hole mass, $m\_p$ the mass of a proton and $\sigma\_T$ is the Thomson scattering cross-section for free electrons (the major source of opacity in the infalling hot gas).

The biggest supermassive black holes in the universe have $M \simeq 10^{10}M\_{\odot}$ and thus the Eddington accretion rate for such objects is about $1.4\times 10^{25}$ kg/s or about 2.3 Earths/second or 140 Earths per minute. The difference between this estimate and the one on the wikipedia page could be what is assumed for the biggest $M$ or that $\epsilon$ is a bit smaller than 0.1 or indeed that the luminosity could exceed the Eddington luminosity (because the accretion isn't spherical).

Perhaps a simpler way to get the answer is to find the most luminous quasar and divide by $\epsilon c^2$. The most luminous quasar ever seen is probably something like [3C 454.3](http://www.mdpi.com/2075-4434/5/1/3/pdf), which reaches $\sim 5\times 10^{40}$ Watts in its highest state. Using $\epsilon = 0.1$ yields about an Earth mass per second for the accretion rate.

So perhaps the number on the wikipedia page is a *little* exaggerated.

> **Comments:**
> **username_0**: Great answer! Your link to 3C 454.3 (http://www.mdpi.com/2075-4434/5/1/3/pdf) doesn't work.  EDIT: Just found a chached copy at http://webcache.googleusercontent.com/search?q=cache:iafbgurch_wJ:www.mdpi.com/2075-4434/5/1/3/pdf+&cd=12&hl=en&ct=clnk&gl=nz  
> **username_0**: Using your equation for M-dot, and the mass of 3C273 of 886 million solar masses I get 1.24E18 kg/s. Does that sound right? For the Thomson scattering cross-section I used 6.65E-29 m^2  
> **username_2**: @Jim421616 No, you forgot the factor of a million!  
> **username_0**: Oh yes, I just saw that I used the wrong mass for solar :)  

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### Answer by username_1 on 2018-07-04. Score: 2

Here is a study from 2012 for the largest recorded quasar which quotes an output of 400 times the mass of the sun per year, which is 253 earth masses per minute (133178400 M ⊕ / 525600 mins) at 2.5 percent the speed of light, located 1 billion light years away.

<https://vtnews.vt.edu/articles/2012/11/112912-science-quasar.html>

It's the largest recorded quasar, I don't know the figure for the largest theoretical quasar, there are apparently [hundreds of people](http://www.dailygalaxy.com/my_weblog/2012/11/monster-quasar-discovered-with-power-outflow-100-times-milky-way-galaxy.html) theorizing and debating the theoretical maximum.

[![SDSS J1106+1939](https://i.sstatic.net/t2wst.jpg "SDSS J1106+1939")](https://i.sstatic.net/t2wst.jpg "SDSS J1106+1939")

> **Comments:**
> **username_2**: The question asks about the mass accretion rate, not the size of any outflow.  

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