How much of galaxy redshift is due to gravity?

[very_curious]

Hi,

I'm trying to get my head around theories of the universe, and am wondering if Hubbles Law has been mis-understood.

I know that light from far away galaxies has been redshifted i.e. has lost energy.

But I'm not convinced that this means those galaxies are moving away from us.

What % of the energy loss can be put down to gravitational redshift?

And if galaxies might have more mass in them than we thought (as indicated by galaxy rotation curves), could all of the redshift be explained by the pull of gravity on the escaping light?

Cheers,

 

[jamjr1979]

The red shift in the light from the galaxies is old so, how can we possibly know? Any answer is going to be relative to current data not future. Our closest galaxy, Andromeda, is currently seen in blue shift, so go figure. Using current working models and unknown variables like dark energy and matter leave it open to interpretation in my opinion. Yours is as good as any. Didn't get the percentage sorry.

 

[bcrowell]

FAQ: What does general relativity say about the relative velocities of objects that are far away from one another?

Nothing. General relativity doesn't provide a uniquely defined way of measuring the velocity of objects that are far away from one another. For example, there is no well defined value for the velocity of one galaxy relative to another at cosmological distances. You can say it's some big number, but it's equally valid to say that they're both at rest, and the space between them is expanding. Neither verbal description is preferred over the other in GR. Only local velocities are uniquely defined in GR, not global ones.

Confusion on this point is at the root of many other problems in understanding GR:

Question: How can distant galaxies be moving away from us at more than the speed of light?

Answer: They don't have any well-defined velocity relative to us. The relativistic speed limit of c is a local one, not a global one, precisely because velocity isn't globally well defined.

Question: Does the edge of the observable universe occur at the place where the Hubble velocity relative to us equals c, so that the redshift approaches infinity?

Answer: No, because that velocity isn't uniquely defined. For one fairly popular definition of the velocity (based on distances measured by rulers at rest with respect to the Hubble flow), we can actually observe galaxies that are moving away from us at >c, and that always have been moving away from us at >c.[Davis 2004]

Question: A distant galaxy is moving away from us at 99% of the speed of light. That means it has a huge amount of kinetic energy, which is equivalent to a huge amount of mass. Does that mean that its gravitational attraction to our own galaxy is greatly enhanced?

Answer: No, because we could equally well describe it as being at rest relative to us. In addition, general relativity doesn't describe gravity as a force, it describes it as curvature of spacetime.

Question: How do I apply a Lorentz transformation in general relativity?

Answer: General relativity doesn't have global Lorentz transformations, and one way to see that it can't have them is that such a transformation would involve the relative velocities of distant objects. Such velocities are not uniquely defined.

Question: How much of a cosmological redshift is kinematic, and how much is gravitational?

Answer: The amount of kinematic redshift depends on the distant galaxy's velocity relative to us. That velocity isn't uniquely well defined, so you can say that the redshift is 100% kinematic, 100% gravitational, or anything in between.

Davis and Lineweaver, Publications of the Astronomical Society of Australia, 21 (2004) 97, msowww.anu.edu.au/~charley/papers/DavisLineweaver04.pdf

 

[bcrowell]

The red shift in the light from the galaxies is old so, how can we possibly know?

Just because the light is old, that doesn't mean we can't interpret it properly.

Any answer is going to be relative to current data not future.

You could say this about any other topic in science. Cosmology is in fact a high-precision science these days. We understand more about cosmology than we do about the recent extinctions of many species of frogs or about high-temperature superconductivity.

Our closest galaxy, Andromeda, is currently seen in blue shift, so go figure.

This has no special cosmological implications. Cosmology deals with much larger scales.

Using current working models and unknown variables like dark energy and matter leave it open to interpretation in my opinion.

The physical explanation for cosmological redshifts is well understood. The explanation just doesn't happen to break down naturally into gravitational or kinematic redshifts.

 

[jamjr1979]

Space expanding galaxies apart is the best bet when it comes to inflationary theory, great for the horizon problem. The contrast in blue shift with Andromeda wasn't implying that it was leading me to believe anything particular, should have said that. Galaxies should fly apart according to mass and spin. They don't fly apart though. I never rule out anything. The semantics of relative observations aside, I believe they are moving apart at 5.5 million miles an hour relative to one another to increase to 11 at the next juncture and so and so forth.

 

[Vanadium 50]

Andromeda is blue-shifted, so the answer is "little to none".

 

[bcrowell]

Andromeda is blue-shifted, so the answer is "little to none".

The OP asked about cosmological redshifts, i.e., redshifts from galaxies lying at cosmological distances from us. Andromeda is part of the local group.

 

[Vanadium 50]

True, but if the redshift were due to galactic gravity, we'd see it in all galaxies. We don't.

 

[Tanelorn]

Vanadium, agreed.

Would you have an answer to the question whether galaxies at the edge of the universe moving near the speed of light in our frame of reference have relativisitic mass which produces gravitational pull on the light from them slowing it down? Would this not add to the doppler effect? And perhaps make the rate of expansion appear greater than it really is?

 

[very_curious]

Hi everyone,

Thanks for the initial thoughts, although it doesn't quite answer my question.

If I'm hearing this right, the short answer is that "we don't know"?

Vanadium, I don't buy your answer, as we're talking about the interpretation of an effect rather than the effect itself.

Light from Andromeda is blue-shifted, yes. But it could be that the light is blue-shifted due to kinematic effects, and also red-shifted due to gravitational effects, and the NET effect is a blue-shift.

The same could be true for other star systems/galaxies, but the % influence of the gravitational and kinematic effects could vary. Hence why I asked for a %.

I can also give more context, in terms of where I'm going with this. If all of the redshift can be explained by gravity, then there is no evidence for the fact that galaxies are moving away from us. The key piece of evidence for the Big Bang theory ceases to be a piece of evidence. It weakens the theory, and this matters.

On that note, cosmic background radiation isn't a really a piece of evidence for the Big Bang theory either. CMB has only been observed in our Solar System - because that's where our measuring instruments are. There's nothing to say it exists everywhere.

Any advance on what % of the redshift could be due to gravity. Could it be more than 80%?

 

[Vanadium 50]

"Relativistic mass" is a deprecated name for "energy" and it is not the source of gravity.

 

[very_curious]

Understood.

Sorry, I should have been clearer. I'm not claiming that the galaxies' relativistic mass is the source of their gravity, and hence the source of the redshift.

The source of gravity is the mass within the galaxy. Wouldn't this have an effect on the light that the galaxy emits?

As far as I understand it, my question is still valid - any guidance?

 

[bcrowell]

True, but if the redshift were due to galactic gravity, we'd see it in all galaxies. We don't.

We're talking about two different scales here.

On small scales, spacetime is approximately flat so it makes sense to talk about redshifts as kinematic or gravitational, and the answer is that they're mainly gravitational. The distance from our galaxy to Andromeda is on this scale.

On large scales, all galaxies have redshifts, spacetime can't be approximated as flat, and the redshifts cannot be unambiguously ascribed to either kinematic or gravitational effects, for the reasons explained in #3.

 

[bcrowell]

If I'm hearing this right, the short answer is that "we don't know"?

The short answer is that the question is inherently a question that doesn't make sense. Asking whether cosmological redshifts are kinematic or gravitational is like asking whether democracy smells like peppermint or spearmint. I'm not saying that it's a stupid question or a bad question. It's a very natural, intelligent question. I would guess that it was the kind of question that topnotch physicists would have asked around 1920. It just doesn't happen to be a meaningful question in the context of what we now know about GR.

For comparison, consider the question of what path an electron travels in a hydrogen atom. It seemed like a reasonable question to Bohr, but we now know that it's a question that isn't meaningful. A trajectory isn't something that an electron has.

We know exactly why cosmological redshifts exist. There is no mystery. GR explains them perfectly. The "why" just doesn't happen to fit into the categories of kinematic or gravitational.

The source of gravity is the mass within the galaxy. Wouldn't this have an effect on the light that the galaxy emits?

Are you talking about the gravitational redshift that happens because the photon has to climb out of the potential well of the galaxy containing the star from which it was emitted? This effect exists, but it's very small compared to cosmological Doppler shifts. If you want to calculate it, you just need to estimate the gravitational potential Gm/r and divide by c². Stick in typical values for the mass and size of a galaxy. Andromeda is near enough that it does make sense to classify its Doppler shift as kinematic or gravitational. Light from Andromeda that we observe here on Earth suffers three Doppler effects: (1) the gravitational Doppler shift from Andromeda's gravity, (2) the gravitational Doppler shift from our galaxy (which would tend to cancel #1), and (3) the kinematic shift. I suspect that #3 is much, much bigger than #1 and #2, but if you like, you can calculate it.

 

[Tim_]

bcrowell -

How can you prove that we are not seeing a distorted view of these red shifts because we're near the edge of the milky way?

How do we accurately calculate the gravitational Doppler shift? I thought there was massive discrepancy as to the mass of a galaxy because of the number of unknowns - (size/number black holes)?

 

[Jonathan Scott]

You can look up the http://en.wikipedia.org/wiki/Milky_Way" galaxy in Wikipedia to get values for mass and radius and calculate the gravitational redshift at a given point as Gm/rc². From what I remember, the shift at the solar system's location due to the Milky way is a few parts per million, that is something like 4 * 10^-6. For comparison, from quick calculations, the shift at the surface of the Earth due to the Earth's potential is about 7 * 10^-10 and at the Earth due to the sun is about 10^-8, assuming I entered the right values into the Google calculator.

 

[marcus]

Hi,

I'm trying to get my head around theories of the universe, and am wondering if Hubbles Law has been mis-understood.

I know that light from far away galaxies has been redshifted i.e. has lost energy.

But I'm not convinced that this means those galaxies are moving away from us.

What % of the energy loss can be put down to gravitational redshift?
...

Brian Powell and Ben Crowell (and Jonathan just now) have already replied precisely and at length. Now it's just a question of people listening and assimilating what's been said.

It's obvious from the expert testimony already that if you are talking percentage of cosmo redshift of distant galaxies, the gravitational contribution is essentially ZERO. And you can even detect that with nearby galaxies because light from deep within is not substantially redder than light from the edges.

Grav redshift depends on depth in a grav potential well. If there is a central mass it depends on how close the source of light is. The redshift is more with sources deeper down in the well.

So if grav redshift were a significant contributor, the galaxy would not have just one redshift it would have all different. Depending where in the galaxy you looked. With galaxies close enough so you can sample light from different parts of them. Good luck!

Grav redshift is just not a major upfront contributor. That is when one is looking at distant galaxies where we measure a substantial cosmological redshift. Where you can measure some it would be out in some decimal place, not the main part.
=================

What Jon did was fun. Use Google calculator to, say, find the grav redshift in light coming from the surface of the sun. I typed this into google search window without the quotes:

"G*mass of sun/(radius of sun*c^2)"

and I got out this:
"(G * mass of the sun) / (radius of the sun * (c^2)) = 2.12324397 × 10-6"

that is a redshift of TWO MILLIONTHS. Tiny tiny.

The grav redshift caused by the mass of the galaxy with the source say 50,000 lightyear out from center would be about the same, since the mass of the galaxy is roughly 700 billion times larger, and the RADIUS is a also about 700 billion times larger. The two approximately cancel!

If you would like to compare the radial dist in the example, 50,000 LY, with the sun's radius, just type this into google box:
"50000 light years/radius of sun"

You will get about 700 billion.

So the grav redshift for a galaxy like ours is tiny tiny, negligible. Compared with the kind of cosmo redshifts we measure like 0.1, 0.5.1.2, 2.5, 7.1 etc etc.

Our picture of the U is based on measurements that are on a totally different size scale than the little grav redshift effects.

 

[zaybu]

For gravitational redshift: Δλ/λ ≈ GM/rc²

For doppler redshift: Δλ/λ ≈ v/c

Some depending on the mass (M) of galaxy, its distance(r) and velocity(v), you can have as in the case of Andromeda, its doppler shift much bigger than its gravitational, and because it's moving towards us, it will be blueshifted instead of redshifted.

 

[very_curious]

Thanks everyone,

But something about this still bugs me.

Why does redshifted light mean the universe is expanding?

Is it because the wavelength of the light has become longer?

And if so, what has this got to do with expansion?

Please explain in short, clear sentences so I can fully understand this.

Cheers,

 

[bcrowell]

Why does redshifted light mean the universe is expanding?

In special relativity, a redshift means that the object is moving away from you. If you look around in all directions and see objects whose light is redshifted, it means all those objects are moving away from you.

In general relativity, you have at least two ways of describing it, neither of which is preferred. You can interpret it the same way as in SR (motion of the emitting galaxy) or you can interpret it by saying that the photons' wavelengths increased because the space they were flying through was expanding (gravitational redshift).

 

[Chronos]

Gravitational redshift is only obvious for photos emitted in the immediate vicinity of condensed matter objects. Galaxies are not dense enough to gravitational redshift photons they emit to any significant extent.

 

[bcrowell]

Gravitational redshift is only obvious for photos emitted in the immediate vicinity of condensed matter objects. Galaxies are not dense enough to gravitational redshift photons they emit to any significant extent.

I'm not talking about local gravitational redshifts due to inhomogeneity, I'm talking about cosmological redshifts in a homogeneous universe. If you choose to describe galaxy A as being at rest and cosmologically distant galaxy B as also being at rest, then the redshift A observes in B's light isn't kinematically Doppler shifted, so you can refer to it as a gravitational Doppler shift. (But of course it's not a gravitational Doppler shift in the sense that one usually computes such a thing from the gravitational potential, which is not something you can define globally in a cosmological spacetime.)

 

[bcrowell]

Brian Powell and Ben Crowell (and Jonathan just now) have already replied precisely and at length. Now it's just a question of people listening and assimilating what's been said.

It's obvious from the expert testimony already that if you are talking percentage of cosmo redshift of distant galaxies, the gravitational contribution is essentially ZERO. And you can even detect that with nearby galaxies because light from deep within is not substantially redder than light from the edges.

Grav redshift depends on depth in a grav potential well. If there is a central mass it depends on how close the source of light is. The redshift is more with sources deeper down in the well.

So if grav redshift were a significant contributor, the galaxy would not have just one redshift it would have all different. Depending where in the galaxy you looked. With galaxies close enough so you can sample light from different parts of them. Good luck!

Grav redshift is just not a major upfront contributor. That is when one is looking at distant galaxies where we measure a substantial cosmological redshift. Where you can measure some it would be out in some decimal place, not the main part.

This may just be a difference in terminology, but I don't quite agree if this is intended to be a characterization of what I've said, for the reasons given in #22. I don't know, maybe I'm creating confusion by using "gravitational redshift" in a sense that is broader than the standard usage.

What I think would be completely incorrect (not that I attribute this to you or Chronos) would be a statement that nearly all of a cosmological redshift is due to relative motion of the source and the observer.

We have three cases:
1) A photon is Doppler shifted as it passes through inhomogeneities such as the gravity wells of an emitting galaxy or a receiving galaxy.
2) A photon is Doppler shifted, and we describe this verbally as happening because galaxy A is verbally described as moving away from cosmologically distant galaxy B.
3) We make the same observations in the same situation as #2, but we verbally describe both galaxies as being at rest.

We all agree that effect #1 can be easily estimated numerically, and is negligible compared to #2 or #3 for photons that travel cosmological distances.

If my usage of "gravitational redshift" is nonstandard, then there needs to be some other term for describing #3. What would it be?

In any case, the distinction between #2 and #3 is a verbal one, not a mathematical, physical, or empirically testable one. We are also free to describe a given cosmological redshift as a 50-50 mixture of #2 and #3 (call it #2.5). We can even say that cosmologically distant galaxies are moving toward us, but their distance from us is increasing because the space in between is expanding so fast (call this #4 or something). Or we can say that space is contracting, but we still observe redshifts rather than blueshifts because cosmologically distant galaxies are moving away from us so fast.

I've started a thread here https://www.physicsforums.com/showthread.php?t=493465 in the relativity forum to ask about terminology.