<p>Let's do the math: the equation for absolute magnitude <span class="math-container">$M$</span> in relation to apparent magnitude <span class="math-container">$m$</span> in relation to distance <span class="math-container">$d$</span> is:</p>
<p><span class="math-container">$m - M = -5 + 5 \log(d)$</span></p>
<p>(You do not need to know how that works as I just looked it up and plugged the numbers in).</p>
<p>The <a href="https://en.wikipedia.org/wiki/Limiting_magnitude" rel="nofollow noreferrer">limiting magnitude</a> for the human eye is about 6th magnitude, so we'll have to calculate for <span class="math-container">$m=6$</span>.</p>
<p>Let's use <a href="https://en.wikipedia.org/wiki/TON_618" rel="nofollow noreferrer">TON 618</a> as the quasar.  It's already one of the most luminous quasars known, so it will be seen in the night sky at a much farther distance than other quasars. (We will revisit other quasars later). Using our formula, TON 618 would need to be about 218.8 million parsecs, or 713 million light years away, to reach magnitude 6. This is about 200 million light years further away than the Cartwheel Galaxy!</p>
<p>Now, let's say you want it to be bright. Placing it at the distance of <a href="https://en.wikipedia.org/wiki/Messier_81" rel="nofollow noreferrer">Bode's Galaxy</a> (11.8 million light-years), TON 618 would reach apparent magnitude -2.91, which is already brighter than every star in the night sky or about as bright as <a href="https://en.wikipedia.org/wiki/Jupiter" rel="nofollow noreferrer">Jupiter</a>. Not bright enough for you?  Let's place it in the <a href="https://en.wikipedia.org/wiki/Large_Magellanic_Cloud" rel="nofollow noreferrer">Large Magellanic Cloud (LMC)</a>, at a distance of about 160 thousand light-years. There, TON 618 would reach magnitude -12.2! Which is about as bright as the full moon or the upcoming Betelguese supernova, bright enough to easily cast shadows on the ground and to be easily seen during the day!</p>
<p>Now, for a more &quot;average&quot; quasar: <a href="https://en.wikipedia.org/wiki/3C_273" rel="nofollow noreferrer">3C 273</a> is the closest quasar to Earth, with an apparent magnitude of 12.9. If we moved it to 113 million light-years away, it would reach magnitude 6 and be faintly visible with the unaided eye. If it were in Bode's Galaxy, it would be at magnitude 1.08, or around the same brightness as the star <a href="https://en.wikipedia.org/wiki/Fomalhaut" rel="nofollow noreferrer">Fomalhaut</a>, or about the same as <a href="https://en.wikipedia.org/wiki/Saturn" rel="nofollow noreferrer">Saturn</a> at minimum brightness. Placing it in the LMC would give it an apparent magnitude of -8.2, which is about as bright as the quarter moon, as bright as Phobos is from the surface of Mars or around 1 magnitude (2.5 times) brignter than <a href="https://en.m.wikipedia.org/wiki/SN_1006" rel="nofollow noreferrer">SN 1006</a>, the brightest supernova ever observed from earth. Which is also visible during the day and able to cast visible shadows on the ground at night!</p>
<p>Keep in mind that 3C 273 is a blazar (which means the jet of the quasar is pointed directly at us) and TON 618 is not, so TON 618 may be brighter if it were facing us. Also, <a href="https://en.wikipedia.org/wiki/Sagittarius_A*" rel="nofollow noreferrer">Sagittarius A*</a> may re-ignite to become a quasar during the Milky Way/Andromeda collision due to the in-fall of gas and dust shot towards it during the galactic merger, so if you survive a few billion years you may get to see that.</p>
<p>Edit: Just did some more math, for an even more luminous quasar and potentially the brightest one ever discovered (SMSS J215728.21-360215.1). It would be faintly visible with the naked eye at a distance of 1.5 <em>billion</em> light years. Placing it at Bode's Galaxy would give it a magnitude of -4.5! Able to cast shadows at night and visible during the day, about as bright as Venus. And placing SMSS J215728.21-360215.1 in the LMC would give it a magnitude of -13.9, that's almost 1 lux of illumination, as bright as Sirius seen from 1700 au (or Sirius if it was 320 times closer!) and would look like a second sun (as if our sun was in a wide binary), even brighter than Alpha Centauri A appears when viewed from Proxima b (planet around binary companion of alpha cent. A).</p>

CC BY-SA 4.0
2024-07-05T14:23:50.567Z
"Siri, set an alarm to check the Sag A* quasar in 5 billion years."
Barmar
CC BY-SA 4.0
2024-07-05T18:19:54.200Z
Thanks for your answer! So my intuition was right, that a quasar in the vicinity would be easily visible to the naked eye! I wonder why there aren't any in the local group.
Joe Peters
CC BY-SA 4.0
2024-07-05T19:05:14.320Z
@JoePeters quasars are usually the result of either a galactic merger or from young galaxies, the reason that most are at great distances is because we are seeing them at a point when the universe was much younger and denser, there was alot of material near the black holes in which they fed, forming a quasar, eventually that material runs out and the bh becomes quiet, during a galactic merger, large amounts of gas and dust can be shot towards the galactic center which may allow them to re-ignite. Basically because most smbh's have cleared out the galactic center of large amounts of dust by now
ArchiveOfStars
CC BY-SA 4.0
2024-07-06T15:47:15.563Z
You should use more capital letters and less significant figures.
Mithoron
CC BY-SA 4.0
2024-07-06T15:47:20.943Z
How much would the visibility depend on the orientation of the quasar? Could there be a sneaky one a few hundreds of light years away that we couldn't detect at present?
Andrew Morton
CC BY-SA 4.0
2024-07-06T16:23:54.723Z
@AndrewMorton no, even though blazars may be brighter, quasars still outshine entire galaxies regardless of orientation plus their high x-ray emissions would make them bright targets for telescopes like chandra, we would know if there was one that close
ArchiveOfStars
CC BY-SA 4.0
2024-07-07T04:38:58.937Z
@Mithoron elaborate on significant figures please? I'll fix the capitalization
ArchiveOfStars
CC BY-SA 4.0
2024-07-07T04:57:38.523Z
@Nick2253 thanks for the edit advice! I kept most of the changes though I did add back most of my comparisons
ArchiveOfStars
CC BY-SA 4.0
2024-07-08T07:43:51.027Z
@ArchiveOfStars Happy to help!  If you're not comfortable with punctuation or the shift key, then, in the future, I'd strongly recommend running what you write through a tool like Grammarly.  That will help you clean up your formatting, grammar, and related.  Also, the comparisons I removed were either non-trivial to verify or non-intuitive, and since the only point of the comparisons is to help contextualize the already confusing concept of apparent magnitude, they seemed to do more harm than good.  However, it's your answer, so it's really up to you how you want to handle them.
Nick2253
CC BY-SA 4.0
2024-07-05T06:10:57.637Z
2024-07-07T04:56:04.933Z
2024-07-07T04:56:04.933Z
ArchiveOfStars
<p>I know that quasars are the most luminous objects known in the universe, but all are at such incredible distances (billions of light years away) that none are visible to the naked eye. I'm wondering, because I would assume if there was one in the local group, it would be, but there isn't.
See <a href="http://wiki.org/quasar" rel="nofollow noreferrer">http://wiki.org/quasar</a></p>

<active-galaxy>
How close would a quasar have to be to be seen with the naked eye?
Joe Peters
# How close would a quasar have to be to be seen with the naked eye?

(Asked by: username_0 on 2024-07-05)

I know that quasars are the most luminous objects known in the universe, but all are at such incredible distances (billions of light years away) that none are visible to the naked eye. I'm wondering, because I would assume if there was one in the local group, it would be, but there isn't.
See <http://wiki.org/quasar>

**Tags:** active-galaxy


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## 1 answers

### Answer by username_1 on 2024-07-05. Score: 11

Let's do the math: the equation for absolute magnitude $M$ in relation to apparent magnitude $m$ in relation to distance $d$ is:

$m - M = -5 + 5 \log(d)$

(You do not need to know how that works as I just looked it up and plugged the numbers in).

The [limiting magnitude](https://en.wikipedia.org/wiki/Limiting_magnitude) for the human eye is about 6th magnitude, so we'll have to calculate for $m=6$.

Let's use [TON 618](https://en.wikipedia.org/wiki/TON_618) as the quasar. It's already one of the most luminous quasars known, so it will be seen in the night sky at a much farther distance than other quasars. (We will revisit other quasars later). Using our formula, TON 618 would need to be about 218.8 million parsecs, or 713 million light years away, to reach magnitude 6. This is about 200 million light years further away than the Cartwheel Galaxy!

Now, let's say you want it to be bright. Placing it at the distance of [Bode's Galaxy](https://en.wikipedia.org/wiki/Messier_81) (11.8 million light-years), TON 618 would reach apparent magnitude -2.91, which is already brighter than every star in the night sky or about as bright as [Jupiter](https://en.wikipedia.org/wiki/Jupiter). Not bright enough for you? Let's place it in the [Large Magellanic Cloud (LMC)](https://en.wikipedia.org/wiki/Large_Magellanic_Cloud), at a distance of about 160 thousand light-years. There, TON 618 would reach magnitude -12.2! Which is about as bright as the full moon or the upcoming Betelguese supernova, bright enough to easily cast shadows on the ground and to be easily seen during the day!

Now, for a more "average" quasar: [3C 273](https://en.wikipedia.org/wiki/3C_273) is the closest quasar to Earth, with an apparent magnitude of 12.9. If we moved it to 113 million light-years away, it would reach magnitude 6 and be faintly visible with the unaided eye. If it were in Bode's Galaxy, it would be at magnitude 1.08, or around the same brightness as the star [Fomalhaut](https://en.wikipedia.org/wiki/Fomalhaut), or about the same as [Saturn](https://en.wikipedia.org/wiki/Saturn) at minimum brightness. Placing it in the LMC would give it an apparent magnitude of -8.2, which is about as bright as the quarter moon, as bright as Phobos is from the surface of Mars or around 1 magnitude (2.5 times) brignter than [SN 1006](https://en.m.wikipedia.org/wiki/SN_1006), the brightest supernova ever observed from earth. Which is also visible during the day and able to cast visible shadows on the ground at night!

Keep in mind that 3C 273 is a blazar (which means the jet of the quasar is pointed directly at us) and TON 618 is not, so TON 618 may be brighter if it were facing us. Also, [Sagittarius A\*](https://en.wikipedia.org/wiki/Sagittarius_A*) may re-ignite to become a quasar during the Milky Way/Andromeda collision due to the in-fall of gas and dust shot towards it during the galactic merger, so if you survive a few billion years you may get to see that.

Edit: Just did some more math, for an even more luminous quasar and potentially the brightest one ever discovered (SMSS J215728.21-360215.1). It would be faintly visible with the naked eye at a distance of 1.5 *billion* light years. Placing it at Bode's Galaxy would give it a magnitude of -4.5! Able to cast shadows at night and visible during the day, about as bright as Venus. And placing SMSS J215728.21-360215.1 in the LMC would give it a magnitude of -13.9, that's almost 1 lux of illumination, as bright as Sirius seen from 1700 au (or Sirius if it was 320 times closer!) and would look like a second sun (as if our sun was in a wide binary), even brighter than Alpha Centauri A appears when viewed from Proxima b (planet around binary companion of alpha cent. A).

> **Comments:**
> **username_2**: "Siri, set an alarm to check the Sag A* quasar in 5 billion years."  
> **username_0**: Thanks for your answer! So my intuition was right, that a quasar in the vicinity would be easily visible to the naked eye! I wonder why there aren't any in the local group.  
> **username_1**: @JoePeters quasars are usually the result of either a galactic merger or from young galaxies, the reason that most are at great distances is because we are seeing them at a point when the universe was much younger and denser, there was alot of material near the black holes in which they fed, forming a quasar, eventually that material runs out and the bh becomes quiet, during a galactic merger, large amounts of gas and dust can be shot towards the galactic center which may allow them to re-ignite. Basically because most smbh's have cleared out the galactic center of large amounts of dust by now  
> **username_3**: You should use more capital letters and less significant figures.  
> **username_4**: How much would the visibility depend on the orientation of the quasar? Could there be a sneaky one a few hundreds of light years away that we couldn't detect at present?  
> **username_1**: @AndrewMorton no, even though blazars may be brighter, quasars still outshine entire galaxies regardless of orientation plus their high x-ray emissions would make them bright targets for telescopes like chandra, we would know if there was one that close  
> **username_1**: @username_3 elaborate on significant figures please? I'll fix the capitalization  
> **username_1**: @username_5 thanks for the edit advice! I kept most of the changes though I did add back most of my comparisons  
> **username_5**: @username_1 Happy to help!  If you're not comfortable with punctuation or the shift key, then, in the future, I'd strongly recommend running what you write through a tool like Grammarly.  That will help you clean up your formatting, grammar, and related.  Also, the comparisons I removed were either non-trivial to verify or non-intuitive, and since the only point of the comparisons is to help contextualize the already confusing concept of apparent magnitude, they seemed to do more harm than good.  However, it's your answer, so it's really up to you how you want to handle them.  

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