<p>Firstly, the figure you quote is disputed and must have very substantial uncertainties. The same wikipedia article also cites 3 per century.</p>

<p>Second, and more importantly, you have not accounted for dust obscuration. Most type II supernovae will occur in massive stars close to the Galactic plane and will be afflicted by huge amounts of extinction. </p>

<p>If we assume an peak absolute magnitude of about -18 and visual extinction of 2 mag per kpc in the galactic plane, then a supernova would have to be within a few kpc to be a notable naked eye object.</p>

<p>If we consider the Milky Way disc to be of radius 15kpc, then a horizon at say 3kpc only encompasses 4% of the possible volume. Thus if there are say 4 per century, only 0.16 per century would be notable naked eye objects.</p>

CC BY-SA 4.0
2018-09-28T13:27:38.453Z
`Thus if there are say 4 per century, only 0.16 per century would be notable naked eye objects`
You are breaking my heart :(
Matthieu Charbonnier
CC BY-SA 3.0
2016-06-04T20:28:01.973Z
2016-06-04T20:28:01.973Z
ProfRob
<p>Some supernovæ are more super than others, but that is not the reason that we have not observed one in 300 years. There have been 5 or 6 naked eye supernovae in the last 1000 years, There have certainly been others (such as Cassiopeia A and <a href="https://en.wikipedia.org/wiki/G1.9%2B0.3" rel="nofollow">Supernova remnant G1.9+0.3</a> But they have have been hidden by the dense dust and gas in the plane of the galaxy. Some regions of the centre of the galaxy have 30 magnitudes of extinction in visible light. That means that a SN with a magnitude of 0, would appear to have magnitude 30, and be essentially invisible.</p>

<p>So while we have been unlucky: we should probably expect to have seen a couple of supernovae since Kepler's star, the probability is not so very small.</p>

CC BY-SA 3.0
2016-06-04T19:34:03.827Z
2016-06-04T19:34:03.827Z
James K
<p>Also, you might be forgetting that the distances of the stars that exploded will cause us to see them at different times.  Say three stars exploded in a given year but one was 1,000 light years away another was 1,500 light years away and the third was 2,000 light years away.  We wouldn't see those novae here on Earth in the same year.  So, while it's quite possible that there are 2 to 3 novae a year, we may (i.e. likely will) see them many years apart.  </p>

<p>On the flip side, a star that exploded 100 years ago that was 100 light years away and another star that exploded 500 years ago and was 500 light years away would appear to us in the same year here on Earth.</p>

CC BY-SA 3.0
2016-09-06T22:37:43.420Z
@KeithThompson If you don't see the problem with your logic I'm not sure that I can describe it to you further.  If we take your example of 1 per century then the number we actually see on earth will be skewed by the spatial distribution of the events.  Some centuries we will see 1, some we will see none, and some we will see several.  Over a long period of time the average would certainly tend to 1.  The OP's question was why would we not see any in certain or even possibly multiple centuries and spatial distribution is one reason.
HisDivineShadow
CC BY-SA 3.0
2016-09-06T22:45:13.933Z
Yes, the average would tend to 1 -- and that's assuming there's exactly 1 supernova every 100 years. But in fact there isn't; they're more or less randomly distributed both in time and in space. Assume there's an average of 1 supernova per century, occurring at random times and places within the Milky Way. If we saw them as they occurred, we'd see an average of 1 supernova every 100 years, with a random distribution. With a finite speed of light, again, we'd see an average of 1 supernova every 100 years, with essentially *the same* random distribution. There is no net effect.
Keith Thompson
CC BY-SA 3.0
2016-08-26T17:45:48.830Z
True, but not particularly relevant. If we have, say, 1 supernova every 100 years, and they're distributed randomly, then we'll see approximately 1 supernova every 100 years (ignoring the fact that some are hidden by gas and/or dust). The 10 we see in a given millennium just won't have exploded within 1000 years of each other, but the *rate* will be about the same.
Keith Thompson
CC BY-SA 3.0
2016-08-26T18:10:18.510Z
@KeithThompson  we won't necessarily see one a year even if they are distributed randomly because a spatially random distribution would not create the same time distribution on earth.  Hence, we would likely see clumps of novas and periods of none.
HisDivineShadow
CC BY-SA 3.0
2016-08-26T18:17:48.283Z
"Clumps of [super]novas and periods of none" is entirely consistent with a random (spacial and/or temporal) distribution. My point is that, assuming the rate of supernovas is reasonably consistent over time, the fact that it takes up to several tens of thousands of years for the light to get to us does not affect the expected frequency or distribution of supernovas seen from Earth. Statistically, it all evens out over time.
Keith Thompson
CC BY-SA 3.0
2016-08-26T20:46:35.890Z
@KeithThompson "it all evens out over time" that doesn't make sense in the context of your argument.  The issue is not whether the occurrence of supernova over a long period of time will even out it's why haven't there been any in the short time span of a couple centuries.  One explanation is the one that I gave.  The scarcity of supernova means that the deviation from the mean will likely be large in any event and the spatial distribution of the supernova as seen from earth could have a dramatic effect on it.
HisDivineShadow
CC BY-SA 3.0
2016-08-26T20:55:40.147Z
Suppose there's 1 visible supernova on average in the Milky Way every 100 years. If light were infinitely fast, we'd expect to see on average 1 supernova every 100 years. Given the finite speed of light, each visible supernova would be delayed by up to, say, 70,000 years.  But the average frequency of supernovas seen from Earth would be unchanged; it would still be 1 every 100 years. If you disagree, please explain whether we would expect to see supernova more or less frequently, and why.
Keith Thompson
CC BY-SA 4.0
2019-04-12T12:30:03.187Z
You could write a simple program to simulate this, to see if your hypothesis is valid... Or maybe @Keith should write it, since it appears he has a lot of coding experience. ;)
PM 2Ring
CC BY-SA 3.0
2016-08-26T15:42:19.813Z
2016-08-26T17:20:35.923Z
2016-08-26T17:20:35.923Z
HisDivineShadow
<blockquote>
  <p>So from this I can only come to the conclusion that supernovae did in
  fact happen in the Milky Way in the last two centuries, but that we
  didn't see any of them.</p>
  
  <p>But now I'm confused. I read about supernovae that have happened in
  galaxies billions of light-years from here that lit up as the
  brightest source of light in the sky for days. Surely we would be able
  to see all of the supernovae that happen in our Milky Way</p>
</blockquote>

<p>One problem with estimating how many supernovae have happened in the Milky Way in the last two centuries, is that the remnant from a supernova is far dimmer than the nova itself and far harder to find. Several supernovae could have happened in the Milky Way in the last 2 centuries and remain undiscovered — and just for clarity, we define the date of a supernova by the date the light from the explosion reaches the Earth, so saying saying a nova "happened" in the last 200 years refers to the date the light from the event reached Earth, not the actual date of the event, which you probably already know, but just to clarify. </p>

<p>So for argument's sake, let's say that a supernova's light reached the Earth about 50 years ago, but it took place on the far side of the galaxy. To find that, we'd have to look for a nebula on the far side of the galaxy and that's a hard thing to see. Similar to looking for the theoretical Planet Nine, finding old supernova remnants on the other side of the Milky Way takes a lot of looking. Even with modern telescopes, it's still a needle in a haystack, and especially if the view is blocked by dust like much of the Milky Way is.</p>

<p>A Milky Way supernova remnant was discovered in 1985, <a href="https://en.wikipedia.org/wiki/G1.9%2B0.3" rel="noreferrer">supernova remnant G1.9+0.3</a>. It was thought to have "happened" around 1868, though it went unobserved and probably wasn't visible to the naked eye at the time.   There's probably been several others more recent than that one.  G1.9+0.3 would have been visible if not for interstellar dust. From article above:</p>

<blockquote>
  <p>It was a type Ia supernova believed to have exploded about 25,000
  years ago, and the signal began reaching Earth around 1868. The light
  from the supernova would have been visible to 19th century
  astronomers, had it not been obscured by the dense gas and dust of the
  Galactic Center.</p>
</blockquote>

<p>I'm not sure the 4.6 supernovae per century from your article is accurate. It might be, but the number I'm used to hearing is about one per century. But regardless of which number is actually correct, it still doesn't imply high mathematical improbability because many Milky Way novae would have gone unnoticed if they were far enough away. In short, I agree with what you said here:</p>

<blockquote>
  <p>I can only come to the conclusion that supernovae did in fact happen in the Milky Way in the last two centuries, but that we didn't see any of them.</p>
</blockquote>

<p>Here's a related <a href="http://www.universetoday.com/120006/why-cant-we-see-the-center-of-the-milky-way/" rel="noreferrer">article on Milky Way visibility</a>.</p>

<p>Observation of a distant galaxy nova is possible if we have telescopes looking in that direction. A nova is much more detectable at the time it goes nova.  Much less so, years later.</p>

<p>Today, however, with <a href="https://en.wikipedia.org/wiki/Supernova_Early_Warning_System" rel="noreferrer">neutrino detection in 7 locations around the globe</a>, I think it's virtually impossible that we'd miss a supernova in the Milky Way, so we have a good chance of seeing one in our lifetime and it's likely that none have occurred since somewhere around 1980. A <a href="https://en.wikipedia.org/wiki/SN_1987A#Neutrino_emissions" rel="noreferrer">supernova was detected in the Andromeda galaxy in 1987</a> by that method, and our neutrino detection has improved since then to give us early warning and pinpoint location.</p>

<p>As far as visibility, size matters, but what matters more is how close and how much dust is in the way. Most of the recorded supernovae were quite bright and fairly noticeable to someone who was familiar with the stars in the sky (<a href="https://en.wikipedia.org/wiki/List_of_supernovae#List" rel="noreferrer">list of known supernovae</a>).</p>

<p>Eight Milky Way novae have been recorded by history and observed by the naked eye in the last 2,000 years, well below the number that should have happened in that time. Five of those eight had brightness greater than $-3$, which is brighter than Jupiter and would have been immediately noticed by anyone familiar with star charting. Two others had magnitudes around zero, which is still brighter than most stars. <a href="https://en.wikipedia.org/wiki/SN_386" rel="noreferrer">SN386</a> was less bright, but is still easily visible and recorded by Chinese astronomers. And finally, <a href="https://en.wikipedia.org/wiki/Cassiopeia_A" rel="noreferrer">Cassiopeia A</a> was quite dim, but it was still observable. Only about 10% (ballpark estimate) of the Milky Way is close enough and unobstructed enough to provide supernovae that would visibly get noticed.  Most would have gone unnoticed until recently.</p>

<p>Hope that's not too wordy, I can try to clean up if needed.</p>

CC BY-SA 3.0
2016-08-26T16:47:17.580Z
A nova and a supernova are quite different things. I think most of all users of "nova" in your answer should be "supernova".
Keith Thompson
CC BY-SA 3.0
2018-03-04T00:50:14.877Z
SN 1987 was in the Large Magellanic Cloud. Considerably closer than Andromeda.
ProfRob
CC BY-SA 4.0
2019-04-12T12:24:09.697Z
You should edit your answer to comply with the info Keith & Rob mentioned.
PM 2Ring
CC BY-SA 3.0
2016-06-04T19:34:27.553Z
2016-06-04T22:48:26.247Z
2016-06-04T22:48:26.247Z
userLTK
<p>I found this on the Wikipedia page on <a href="https://en.wikipedia.org/wiki/Supernova" rel="nofollow noreferrer">supernovae</a>:</p>

<blockquote>
  <p>The total supernova rate in our galaxy is estimated to be about 4.6 per century, or one every 22 years, although <strong>we haven't actually observed one</strong> for several centuries.</p>
</blockquote>

<p>That sounds like a freak occurrence to me.</p>

<p>It made me curious about the numbers so I refreshed my knowledge on the Poisson distribution. It is not specified how many centuries we have not seen a supernova, but let's assume it's only two.</p>

<p>If on average 9.2 supernovae happen per 2 centuries then the chance of having exactly 9 in any two century period can be calculated with:</p>

<p><span class="math-container">$$p(k) = {\lambda^k \times e^{-\lambda} \over k!}$$</span></p>

<p>Filling in <span class="math-container">$k=9$</span>,</p>

<p><span class="math-container">$$p(9) = {9.2^9 \times e^{-9.2} \over 9!}=0.1315$$</span></p>

<p>The chance that there is not a single supernova in a two century period is:</p>

<p><span class="math-container">$$p(0) = {9.2^0 \times e^{-9.2} \over 0!}=0.00010104$$</span></p>

<p>That's about a 1 in 10,000 chance. If "several" means 3 centuries, then the chance of not having any supernova is as little as 1 in 100,000.</p>

<p>So from this I can only come to the conclusion that supernovae did in fact happen in the Milky Way in the last two centuries, but that we didn't <em>see</em> any of them.</p>

<p>But now I'm confused. I read about supernovae that have happened in galaxies billions of light-years from here that lit up as the brightest source of light in the sky for days. Surely we would be able to see <em>all</em> of the supernovae that happen in our Milky Way (no more than 100,000 light years away) with the naked eye, let alone with telescopes?</p>

<p>Are some supernovae so much more <em>super</em> than others? Are all of the Milky Way's supernovae visible to the naked eye?</p>

CC BY-SA 3.0
2016-06-04T17:48:50.747Z
An interesting counterexample is [Cassiopeia A](https://en.wikipedia.org/wiki/Cassiopeia_A), which wouldn't have been widely visible to observers on Earth because dust absorbed most of the light emitted in the *visible* part of the spectrum. There is some evidence that a few observations were made (this would have been in the 17th century), but there isn't any definitive evidence.
HDE 226868
<light><distances><supernova>
Why don't we see more supernovae in our galaxy?
mgr326639
# Why don't we see more supernovae in our galaxy?

(Asked by: username_0 on 2016-06-04)

I found this on the Wikipedia page on [supernovae](https://en.wikipedia.org/wiki/Supernova):

> The total supernova rate in our galaxy is estimated to be about 4.6 per century, or one every 22 years, although **we haven't actually observed one** for several centuries.

That sounds like a freak occurrence to me.

It made me curious about the numbers so I refreshed my knowledge on the Poisson distribution. It is not specified how many centuries we have not seen a supernova, but let's assume it's only two.

If on average 9.2 supernovae happen per 2 centuries then the chance of having exactly 9 in any two century period can be calculated with:

$$p(k) = {\lambda^k \times e^{-\lambda} \over k!}$$

Filling in $k=9$,

$$p(9) = {9.2^9 \times e^{-9.2} \over 9!}=0.1315$$

The chance that there is not a single supernova in a two century period is:

$$p(0) = {9.2^0 \times e^{-9.2} \over 0!}=0.00010104$$

That's about a 1 in 10,000 chance. If "several" means 3 centuries, then the chance of not having any supernova is as little as 1 in 100,000.

So from this I can only come to the conclusion that supernovae did in fact happen in the Milky Way in the last two centuries, but that we didn't *see* any of them.

But now I'm confused. I read about supernovae that have happened in galaxies billions of light-years from here that lit up as the brightest source of light in the sky for days. Surely we would be able to see *all* of the supernovae that happen in our Milky Way (no more than 100,000 light years away) with the naked eye, let alone with telescopes?

Are some supernovae so much more *super* than others? Are all of the Milky Way's supernovae visible to the naked eye?

**Tags:** light, distances, supernova
> **Comments:**
> **username_1**: An interesting counterexample is [Cassiopeia A](https://en.wikipedia.org/wiki/Cassiopeia_A), which wouldn't have been widely visible to observers on Earth because dust absorbed most of the light emitted in the *visible* part of the spectrum. There is some evidence that a few observations were made (this would have been in the 17th century), but there isn't any definitive evidence.  

---

## 4 answers

### Answer by username_8 on 2016-06-04. Score: 10 | Accepted answer

> So from this I can only come to the conclusion that supernovae did in
> fact happen in the Milky Way in the last two centuries, but that we
> didn't see any of them.
>
> But now I'm confused. I read about supernovae that have happened in
> galaxies billions of light-years from here that lit up as the
> brightest source of light in the sky for days. Surely we would be able
> to see all of the supernovae that happen in our Milky Way

One problem with estimating how many supernovae have happened in the Milky Way in the last two centuries, is that the remnant from a supernova is far dimmer than the nova itself and far harder to find. Several supernovae could have happened in the Milky Way in the last 2 centuries and remain undiscovered — and just for clarity, we define the date of a supernova by the date the light from the explosion reaches the Earth, so saying saying a nova "happened" in the last 200 years refers to the date the light from the event reached Earth, not the actual date of the event, which you probably already know, but just to clarify.

So for argument's sake, let's say that a supernova's light reached the Earth about 50 years ago, but it took place on the far side of the galaxy. To find that, we'd have to look for a nebula on the far side of the galaxy and that's a hard thing to see. Similar to looking for the theoretical Planet Nine, finding old supernova remnants on the other side of the Milky Way takes a lot of looking. Even with modern telescopes, it's still a needle in a haystack, and especially if the view is blocked by dust like much of the Milky Way is.

A Milky Way supernova remnant was discovered in 1985, [supernova remnant G1.9+0.3](https://en.wikipedia.org/wiki/G1.9%2B0.3). It was thought to have "happened" around 1868, though it went unobserved and probably wasn't visible to the naked eye at the time. There's probably been several others more recent than that one. G1.9+0.3 would have been visible if not for interstellar dust. From article above:

> It was a type Ia supernova believed to have exploded about 25,000
> years ago, and the signal began reaching Earth around 1868. The light
> from the supernova would have been visible to 19th century
> astronomers, had it not been obscured by the dense gas and dust of the
> Galactic Center.

I'm not sure the 4.6 supernovae per century from your article is accurate. It might be, but the number I'm used to hearing is about one per century. But regardless of which number is actually correct, it still doesn't imply high mathematical improbability because many Milky Way novae would have gone unnoticed if they were far enough away. In short, I agree with what you said here:

> I can only come to the conclusion that supernovae did in fact happen in the Milky Way in the last two centuries, but that we didn't see any of them.

Here's a related [article on Milky Way visibility](http://www.universetoday.com/120006/why-cant-we-see-the-center-of-the-milky-way/).

Observation of a distant galaxy nova is possible if we have telescopes looking in that direction. A nova is much more detectable at the time it goes nova. Much less so, years later.

Today, however, with [neutrino detection in 7 locations around the globe](https://en.wikipedia.org/wiki/Supernova_Early_Warning_System), I think it's virtually impossible that we'd miss a supernova in the Milky Way, so we have a good chance of seeing one in our lifetime and it's likely that none have occurred since somewhere around 1980. A [supernova was detected in the Andromeda galaxy in 1987](https://en.wikipedia.org/wiki/SN_1987A#Neutrino_emissions) by that method, and our neutrino detection has improved since then to give us early warning and pinpoint location.

As far as visibility, size matters, but what matters more is how close and how much dust is in the way. Most of the recorded supernovae were quite bright and fairly noticeable to someone who was familiar with the stars in the sky ([list of known supernovae](https://en.wikipedia.org/wiki/List_of_supernovae#List)).

Eight Milky Way novae have been recorded by history and observed by the naked eye in the last 2,000 years, well below the number that should have happened in that time. Five of those eight had brightness greater than $-3$, which is brighter than Jupiter and would have been immediately noticed by anyone familiar with star charting. Two others had magnitudes around zero, which is still brighter than most stars. [SN386](https://en.wikipedia.org/wiki/SN_386) was less bright, but is still easily visible and recorded by Chinese astronomers. And finally, [Cassiopeia A](https://en.wikipedia.org/wiki/Cassiopeia_A) was quite dim, but it was still observable. Only about 10% (ballpark estimate) of the Milky Way is close enough and unobstructed enough to provide supernovae that would visibly get noticed. Most would have gone unnoticed until recently.

Hope that's not too wordy, I can try to clean up if needed.

> **Comments:**
> **username_6**: A nova and a supernova are quite different things. I think most of all users of "nova" in your answer should be "supernova".  
> **username_2**: SN 1987 was in the Large Magellanic Cloud. Considerably closer than Andromeda.  
> **username_7**: You should edit your answer to comply with the info Keith & Rob mentioned.  

---

### Answer by username_2 on 2016-06-04. Score: 7

Firstly, the figure you quote is disputed and must have very substantial uncertainties. The same wikipedia article also cites 3 per century.

Second, and more importantly, you have not accounted for dust obscuration. Most type II supernovae will occur in massive stars close to the Galactic plane and will be afflicted by huge amounts of extinction.

If we assume an peak absolute magnitude of about -18 and visual extinction of 2 mag per kpc in the galactic plane, then a supernova would have to be within a few kpc to be a notable naked eye object.

If we consider the Milky Way disc to be of radius 15kpc, then a horizon at say 3kpc only encompasses 4% of the possible volume. Thus if there are say 4 per century, only 0.16 per century would be notable naked eye objects.

> **Comments:**
> **username_3**: `Thus if there are say 4 per century, only 0.16 per century would be notable naked eye objects` You are breaking my heart :(  

---

### Answer by username_4 on 2016-06-04. Score: 2

Some supernovæ are more super than others, but that is not the reason that we have not observed one in 300 years. There have been 5 or 6 naked eye supernovae in the last 1000 years, There have certainly been others (such as Cassiopeia A and [Supernova remnant G1.9+0.3](https://en.wikipedia.org/wiki/G1.9%2B0.3) But they have have been hidden by the dense dust and gas in the plane of the galaxy. Some regions of the centre of the galaxy have 30 magnitudes of extinction in visible light. That means that a SN with a magnitude of 0, would appear to have magnitude 30, and be essentially invisible.

So while we have been unlucky: we should probably expect to have seen a couple of supernovae since Kepler's star, the probability is not so very small.


---

### Answer by username_5 on 2016-08-26. Score: -2

Also, you might be forgetting that the distances of the stars that exploded will cause us to see them at different times. Say three stars exploded in a given year but one was 1,000 light years away another was 1,500 light years away and the third was 2,000 light years away. We wouldn't see those novae here on Earth in the same year. So, while it's quite possible that there are 2 to 3 novae a year, we may (i.e. likely will) see them many years apart.

On the flip side, a star that exploded 100 years ago that was 100 light years away and another star that exploded 500 years ago and was 500 light years away would appear to us in the same year here on Earth.

> **Comments:**
> **username_6**: True, but not particularly relevant. If we have, say, 1 supernova every 100 years, and they're distributed randomly, then we'll see approximately 1 supernova every 100 years (ignoring the fact that some are hidden by gas and/or dust). The 10 we see in a given millennium just won't have exploded within 1000 years of each other, but the *rate* will be about the same.  
> **username_5**: @KeithThompson  we won't necessarily see one a year even if they are distributed randomly because a spatially random distribution would not create the same time distribution on earth.  Hence, we would likely see clumps of novas and periods of none.  
> **username_6**: "Clumps of [super]novas and periods of none" is entirely consistent with a random (spacial and/or temporal) distribution. My point is that, assuming the rate of supernovas is reasonably consistent over time, the fact that it takes up to several tens of thousands of years for the light to get to us does not affect the expected frequency or distribution of supernovas seen from Earth. Statistically, it all evens out over time.  
> **username_5**: @KeithThompson "it all evens out over time" that doesn't make sense in the context of your argument.  The issue is not whether the occurrence of supernova over a long period of time will even out it's why haven't there been any in the short time span of a couple centuries.  One explanation is the one that I gave.  The scarcity of supernova means that the deviation from the mean will likely be large in any event and the spatial distribution of the supernova as seen from earth could have a dramatic effect on it.  
> **username_6**: Suppose there's 1 visible supernova on average in the Milky Way every 100 years. If light were infinitely fast, we'd expect to see on average 1 supernova every 100 years. Given the finite speed of light, each visible supernova would be delayed by up to, say, 70,000 years.  But the average frequency of supernovas seen from Earth would be unchanged; it would still be 1 every 100 years. If you disagree, please explain whether we would expect to see supernova more or less frequently, and why.  
> **username_5**: @KeithThompson If you don't see the problem with your logic I'm not sure that I can describe it to you further.  If we take your example of 1 per century then the number we actually see on earth will be skewed by the spatial distribution of the events.  Some centuries we will see 1, some we will see none, and some we will see several.  Over a long period of time the average would certainly tend to 1.  The OP's question was why would we not see any in certain or even possibly multiple centuries and spatial distribution is one reason.  
> **username_6**: Yes, the average would tend to 1 -- and that's assuming there's exactly 1 supernova every 100 years. But in fact there isn't; they're more or less randomly distributed both in time and in space. Assume there's an average of 1 supernova per century, occurring at random times and places within the Milky Way. If we saw them as they occurred, we'd see an average of 1 supernova every 100 years, with a random distribution. With a finite speed of light, again, we'd see an average of 1 supernova every 100 years, with essentially *the same* random distribution. There is no net effect.  
> **username_7**: You could write a simple program to simulate this, to see if your hypothesis is valid... Or maybe @Keith should write it, since it appears he has a lot of coding experience. ;)  

---

