Revealing Secrets of Distant Supernova DES16C2nm: 10.5 Billion Years Ago

[Ziang]

Astronomers said a star named DES16C2nm exploded 10.5 billion years ago.
https://phys.org/news/2018-02-astronomers-reveal-secrets-distant-supernova.html

Do they also mean that at the time the event happened, the star was 10.5 billion light-years away from Earth?

 

[Orodruin]

Do they also mean that at the time the event happened, the star was 10.5 billion light-years away from Earth?

No. Because of the expansion of the Universe, the supernova must have been closer than that when it occurred.

 

[Ziang]

Is there any way to figure out how far the star was at the time it exploded?

 

[Orodruin]

Yes, but not at B-level. Also, the question itself comes along with some assumptions that are not clear at B-level such as how you define ”at the same time”.

 

[Bandersnatch]

One can always use a calculator such as this one:
http://www.einsteins-theory-of-relativity-4engineers.com/LightCone7-2017-02-08/LightCone_Ho7.html
Here, you're interested in an object at redshift z=2 (according to the article), and the output you're looking for is 'D_then'.
So it can be found that the proper distance to the supernova was 5.5 billion light-years at emission and is 17.3 at reception.

 

[Orodruin]

Agreed. I change my answer to ”not at B-level if one wants to know how the computation is actually carried out”.

 

[Ziang]

Yes, I would like to see the computation.
Thanks

 

[Ziang]

Because of the expansion of the Universe,...

Because of the expansion of the Universe, galaxies would get further and further from each other, why they sometimes collide another one?

 

[Bandersnatch]

Yes, I would like to see the computation.
Thanks

See here:
https://www.physicsforums.com/insights/lightcone7-tutorial-part-iii-things-computed/

Because of the expansion of the Universe, galaxies would get further and further from each other, why they sometimes collide another one?

Those galaxies close enough to one another have sufficiently strong mutual gravitational attraction that they become decoupled from expansion (w/r to each other). It's the same reason why e.g. the orbit of Earth around the Sun is not affected by the expansion of the universe. Or stars in a galaxy. Or the atoms in your body.

 

[Ziang]

So D_then = 5.5 billion light-years was the distance between the star and Earth at 10.5 billion years ago?

 

[Bandersnatch]

So D_then = 5.5 billion light-years was the distance between the star and Earth at 10.5 billion years ago?

Between the star and where the solar system would form later, yes.

 

[Ziang]

10.5 billion years ago, the universe was 3.3 billion years old. How could the star be 5.5 billion light-years away from the Milky Way?

 

[Bandersnatch]

Ok., why do you think it couldn't? (I suspect there's some confusion about what big bang was)

 

[Ziang]

The Big Bang theory say the universe now is 13.8 billion years old, so 10.5 billion years ago, the universe was 3.3 billion years old. If the star was 5.5 billion light-years away from the Milky Way at that time, it could move away from the Milky Way at a velocity 1.7c?

 

[Bandersnatch]

The 1.7 c number is not correct, because the individual recession velocities were not constant, being much higher early on in the history of the universe.
But yes, there is no limit on the rate of expansion. The universal speed limit of c is applicable only to special cases (hence 'special' relativity) of flat and static space-times. Expanding universe is not one of those, so you can't apply special relativity. It still works locally, in sufficiently small patches of the universe for the expansion to be ignored. So that regardless of how high the overall rate of expansion is, nothing ever overtakes light.

 

[Orodruin]

The universal speed limit of c is applicable only to special cases (hence 'special' relativity) of flat and static space-times.

This is not completely true. Locally, c is the limit even in GR. One also has to be very careful with being aware of what one means when one says things such as "recession velocity of 1.7c", it is typically a statement that depends on the time- and space-conventions. I do not think we can expect the OP to understand these subtleties at B-level, but I think it is important to point out the caveats.

 

[Bandersnatch]

This is not completely true. Locally, c is the limit even in GR

I tried to include that caveat in my post, two sentences further. Or is it still objectionable the way it is put?

it is typically a statement that depends on the time- and space-conventions.

Right. I sometimes hear this objection, but I don't really understand the reasoning. After all, don't we normally use one set of conventions in cosmology? With specific definitions of e.g. distances and recession velocity?
I think you're making a point that the only real observable is the redshift, and everything else is model-dependent.

 

[Orodruin]

I was just emphasising it.

Right. I sometimes hear this objection, but I don't really understand the reasoning. After all, don't we normally use one set of conventions in cosmology? With specific definitions of e.g. distances and recession velocity?

Yes, typically there is a convention used in cosmology. However, what I am saying that it can help to be aware of there being a convention at all not to take proper distances etc as a unique option. It is fine to use the convention as long as one is aware of that one is using a convention.

 

[Ziang]

So it can be found that the proper distance to the supernova was 5.5 billion light-years at emission and is 17.3 at reception.

Now we have three numbers:
The first one is 10.5 billion years. This number means that the explosion occurred 10.5 billion years ago.
The second one is 5.5 billion light-years. This number means that 10.5 billion years ago, the star was 5.5 billion light-years away from where the solar system would form later.
The last one is 17.3 billion light-years. May you tell me what this number means? Thanks

 

[Bandersnatch]

The third number is the distance to which the source of the light you observe now has managed to recede while its light was en route.
It's the distance to the place where the star exploded, if you were to stop the expansion today, take a measuring stick, and see where it is.

 

[Ziang]

At the time the star exploded, it was 5.5 billion light years away. Why did it take 10.5 billion years for light to come Earth?
This looks like the following example:
I am standing at a point A of a line AB = 300000km.
A UFO is flying away from me. At the time t = 0 at point B, it is passing B and emits a flash. Standing at point A, I see the flash at the time t1 = 1.9s?

 

[Orodruin]

At the time the star exploded, it was 5.5 billion light years away. Why did it take 10.5 billion years for light to come Earth?

Because as the light moved towards us, space expanded. If the Universe would "freeze" at the size it had when the light was emitted, it would have taken 5.5 billion years. If the Universe would have been static at the size it is now, it would have taken 17.3 billion years. The reality is that the Universe expands throughout the travel of the light signal and the maths come out to 10.5 billion years.

Edit: To take a more down-to-earth example. Imagine an ant walking along a rubber band. It can walk along the rubber band with a velocity $v$. As the ant walks, you also stretch the rubber band at a rate $R$, meaning that the distance between any two points separated by $\ell$ on the rubber band grows at $R\ell$. The distance between the ant and any fixed point on the rubber band then changes at a velocity $R\ell - v$, i.e., it does not decrease at the speed $v$, you also need to take into account the stretching of the rubber band.

 

[Ziang]

So if the distance between two objects is increasing . There maybe two possible causes:
1. The space is expanding.
2. The space is not expanding, but either or both objects are moving away.

These two causes are different.

What were scientists based on to conclude that the universe is expanding but not galaxies are moving away?

 

[Orodruin]

So if the distance between two objects is increasing . There maybe two possible causes:
1. The space is expanding.
2. The space is not expanding, but either or both objects are moving away.

These two causes are different.

These two are not as different as you might think. It all comes back to the caveats and conventions that I mentioned earlier in this thread. It depends on how you split space-time into space and time. In the standard convention in cosmology, which is the one that we have exclusively used in this thread, the interpretation is 1. However, you can just as well use a different set of coordinates on space-time that, at least locally, makes 2 the proper interpretation. It all comes down to space and time not being as easily separable as you are probably used to thinking about them. I covered this in a recent Insight, although it is aimed at A-level, not B-level, because these things are difficult to get a grip on.

 

[Ziang]

Let me set up a conceptual experiment:
I am standing at a point A of a line AB = 300000km in a "freezing" space.
A UFO is flying away from me. At the time t = 0 at point B, it is passing B and emits a flash. Standing at point A, I believe I see the flash at the time t₁ = 1s.
Now I replace the UFO with a star in this universe, and similar with the supernova above, I would see the flash at time t_x, which is larger than 1, due to the universe is expanding.
Because t₁ is different from t_x, could I say the expansion of the universe is different from flying away (in a freezing universe)?

 

[Viopia]

Because as the light moved towards us, space expanded. If the Universe would "freeze" at the size it had when the light was emitted, it would have taken 5.5 billion years. If the Universe would have been static at the size it is now, it would have taken 17.3 billion years. The reality is that the Universe expands throughout the travel of the light signal and the maths come out to 10.5 billion years.

Edit: To take a more down-to-earth example. Imagine an ant walking along a rubber band. It can walk along the rubber band with a velocity $v$. As the ant walks, you also stretch the rubber band at a rate $R$, meaning that the distance between any two points separated by $\ell$ on the rubber band grows at $R\ell$. The distance between the ant and any fixed point on the rubber band then changes at a velocity $R\ell - v$, i.e., it does not decrease at the speed $v$, you also need to take into account the stretching of the rubber band.

Thank you for exlaining this in such an understandable way. The only thing I don't yet understand is as follows: When the light was emitted from the exploding supernova it was traveling towards the Earth (which was only 5.5 billion light years way at the time of emission).

The emmitted photon's speed, in relation to the approaching Earth at the time of emmission, was 300.000Km per second because the speed of light is a constant. If the Earth's movement due to space expansion caused the photon to take 10.5 billion years to reach the Earth the photon's speed must have been reduced in relation to the Earth.

In other words if a rocket was accelerating away from the supernova (so that it constantly mantained the same distance from the Earth) and emitted a photon towards the Earth which matched the same energy as the photon emitted by the supernova, in what way could it be said that the supernova emitted photon was any different from the photon emmited from the rocket?

The only difference would be that the photon from the rocket will take 5.5 billion years to reach Earth (because the distance is remaining constant) but the photon from the supernova will take 10.5 billion years (because the distance is increasing). Apart from this there is absolutely no difference in the properties of the photons themselves.

In other words there would be no way of determining which is the supernova photon and which is the rocket photon because both photons have exactly the same energy.

 

[Orodruin]

The emmitted photon's speed, in relation to the approaching Earth at the time of emmission, was 300.000Km per second because the speed of light is a constant.

This statement is not correct. In fact, there is no such thing as a speed relative to a distant object in general relativity. Only local relative speeds.

 

[Viopia]

This statement is not correct. In fact, there is no such thing as a speed relative to a distant object in general relativity. Only local relative speeds.

Thanks for your reply. Could you explain what you mean in more detail because I thought that there's no difference between relative motion and "space expanding" between objects.

 

[Orodruin]

Thanks for your reply. Could you explain what you mean in more detail because I thought that there's no difference between relative motion and "space expanding" between objects.

There is a lot of differemce. It is only locally that it is not distinguishable. Space expanding means that the comoving observers (observers at rest relative to the background radiation) get further and further apart without moving relative to the CMB. The distances are getting larger without the observers moving because it is space itself that is growing.

Now, this is a coordinate dependent interpretation and it is locally (but not globally - ie, only in a relatively small space and time) equivalent to the comoving observers moving apart as discussed in one of my PF Insights, but it is an interpretation in the by far most common coordinate systems used to describe cosmology.

 

[Viopia]

There is a lot of differemce. It is only locally that it is not distinguishable. Space expanding means that the comoving observers (observers at rest relative to the background radiation) get further and further apart without moving relative to the CMB. The distances are getting larger without the observers moving because it is space itself that is growing.

Now, this is a coordinate dependent interpretation and it is locally (but not globally - ie, only in a relatively small space and time) equivalent to the comoving observers moving apart as discussed in one of my PF Insights, but it is an interpretation in the by far most common coordinate systems used to describe cosmology.

 

[Viopia]

There is a lot of differemce. It is only locally that it is not distinguishable.

I am still a bit confused. 10.5 billion light years doesn't seem very local. The following statement was made by one of your gold members ''There's no difference between relative motion and "space expanding" between objects. There is a very common misconception that there is a difference, which has even made it into textbooks, but there isn't actually a difference''.

 

[Bandersnatch]

@Viopia I think, for the purposes of this question, it would be sufficient to know that the recessional velocities and local 'real' (or peculiar) velocities can differ in important ways, but can also be compared in some meaningful ways too.
In particular, it's worth reassuring yourself that if you were to put a really long and rigid ruler between yourself and some galaxy receding due to the expansion of space, you would definitely see that galaxy speed past the ruler to ever farther distances. You could also add the local radial velocity of the galaxy (or even a photon) to the recession velocity, just like you would add regular velocity vectors, to obtain a nett velocity that would tell you whether the extra local motion makes the galaxy approach, recede or hover at the same proper distance. I.e. there's an unambiguous physicality here, that you can depend on to visualise what's going on.
At the same time, it's good to keep in mind that there's enough of a difference between the two, that naively extrapolating any further intuitions about velocities should be avoided when thinking about recession.

For example, to bring this into the vicinity of the setup in your question, you can have a rocket moving at such a peculiar (i.e. local) velocity, that the nett approach velocity after adding recession velocity is zero. I.e. the rocket can 'hover' at a constant proper distance from the observer. Just like in your setup - though not for that particular supernova, as it was too far and receding too fast.
For a photon, while locally it always moves at c, it can have any approach velocity whatsoever - including 0 and negative, i.e. being 'stopped' or carried away by expansion despite being sent towards us.

But - here's an example of an important difference - it turns out the redshifts from peculiar velocities and recessional velocities do not add up in the same way. It's not valid to simply add up the two velocities if we want to know the resultant redshift.
A signal, made by the rocket to have the same form at emission as the signal emitted in its rest frame by the supernova it attempts to mimic, and emitted by a rocket with zero approach velocity at the same place and time as the supernova, would not have nett zero redshift, nor would it be redshifted - but would be blueshifted instead.
The details of how this works can be seen here, section III. The figures 5 and 6 can be helpful. (the line marked =(0,0) describe the unaccelerated universe we've assumed here, while =(0.3,0.7) is likely our universe).
So, you would have two photons - one from the supernova, redshifted; another from the rocket, blueshifted. They are therefore distinguishable.

Both photons would arrive on Earth roughly at the same time, as they have the same distance to cover, contrary to your intuition expressed above.
This can be understood by imagining what happens locally, in the immediate vicinity of the supernova. If we arranged for the rocket to emit its photon as it's passing the supernova, we would end up with the two photons traveling together. Since they travel together, in whichever way the expansion affects the intervening space they have to cover, it will do so in the same way for both photons. And since they travel together, and both travel at c, both arrive at the same time, having covered the same distance.

As is mentioned in the article linked earlier, this situation can be observed in nature, with relativistic jets from active galactic nuclei acting out the role of the rocket moving towards Earth, while the faraway galaxies hosting the AGNs are playing the supernova in this scenario.

 

[Viopia]

For a photon, while locally it always moves at c, it can have any approach velocity whatsoever - including 0 and negative, i.e. being 'stopped' or carried away by expansion despite being sent towards us.

Thank you for taking the time to reply in such a detailed way. You have given me so much information that I will need time to digest it all.

 

[Viopia]

For a photon, while locally it always moves at c, it can have any approach velocity whatsoever - including 0 and negative, i.e. being 'stopped' or carried away by expansion despite being sent towards us.

From what you say it appears as though ''space (itself)'' is expanding after all, rather than ''the distance between objects increasing as the objects move apart''. We may be able to do a simple experiment on Earth to prove this. Assume there is a straight train line (track) with distance markers along its length. As we travel along the track (in our track car) at 100mph we pass marker A, and then an hour later we pass marker B, and then an hour later we pass marker C. This means B is 100 miles from A, and C is 200 miles from A. A locomotive passes A at the same time as our car passes B. The locomotive is traveling at 200mph and so when our car has traveled another 100 miles (at C) it is hit from behind by the locomotive. The ''collision'' speed, (ie: the difference in speed between the car and the locomotive) is only 100mph, which is only half of the 200mph that the locomotive is traveling along the track. If we wanted to calculate how fast the locomotive was traveling we could have put two more markers at 1 mile spacings from C towards B. If we check the time the locomotive took to pass these two extra markings we could calculate the speed it was traveling when it crashed into us by measuring how long it took for the locomotive to pass these extra markings (1 mile apart) because we know the distance between them.

CONCLUSION: Can we do the same with the photons emitted from the supernova when they hit the Earth? If we liken emitted photons from the supernova to the locomotive, and the Earth traveling through space to the car (because space itself is expanding) we could calculate how fast the emitted photons are traveling from the supernova (in relation to the Earth) by calculating the time it takes for them to pass each of two added markers spaced at (say) 40,000 metres separation distance from the Earth. The one marker could be suspended 40,000 metres from a balloon, and the other marker could be on, or close to, the Earth's surface. We should suddenly block the emitted photons passing the balloon and measure how long it takes for the last emitted photon to reach the Earth's surface rather than measuring the redshift (we already know what the redshift is). It may be worth checking the speed of the photons emitted from the supernova in this way because if the photon speed is less than the speed of light (less than 299,792 Km per second) space itself is indeed expanding and the distance the supernova emitted photons had traveled when they were received on Earth is 10.5 billion light years. However, if the photon speed is the speed of light itself (actually is 299,792Km per second) space itself is not expanding and the distance the supernova emitted photons had traveled when they were received on Earth is only 5.5 billion light years because the distance between objects is increasing, rather than space itself expanding. I suspect you will you will probably say that the speed of the photons will always be at 299,792 Km per second because they are local to the Earth when they arrive, but I believe this makes little sense. This is a simple experiment to do just to rule this possibility out.

 

[Ibix]

You seem to be proposing a local measurement of the one-way speed of light. The answer depends on your clock synchronisation procedure. The obvious one, which assumes that the speed of light is the same in both directions, will have light passing you at $c$ whatever its source. And a two way measure will be $c$ without assumptions.

There is a difference between local speed measures, which will always return $c$ for a round trip speed, and long-distance speed measures where neither distance traveled nor time taken is particularly well defined. It's that lack of clear definition that makes long distance (Mpc and up) speed measures ill defined, and you cannot replicate it locally.