Dark energy and the kinematic Sunyaev-Zeldovich effect?

[Suekdccia]

TL;DR Summary

Dark energy and the kinematic Sunyaev-Zeldovich effect?

I was reading this interesting article about possible effects of dark energy in the formation of large-scale structures which should have an impact on the Sunyaev-Zeldovich effect ("Dark energy imprints on the kinematic Sunyaev-Zel'dovich signal" (https://arxiv.org/abs/1309.1163))There, the authors indicate that the signal from the kinematic Sunyaev-Zeldovich effect is increased if the equation of state (ω) is more negative than -1 (which is the usual value standarised in ΛCDM), which would mean as far as I understand it that if Dark Energy was stronger or had a bigger density (making ω more negative than -1) then the kSZ effect would be enhanced. However, if ω was less negative than -1 (between 0 and -1) then that would be in a universe with a smalled dark energy density and you say that in such scenario the kSZ effect would be supressed. I have a few question about this:

1. When they say that the kSZ signal is enhanced or supressed what do they exactly mean? That the photons would be blueshifted (in the case where the kSZ in enchanced) or redshifted (in the case where it is surpressed)?
2. If I understood it correctly, if ω was 0, there would be no accelerated expansion and therefore no dark energy of any form. Then in that case, the kSZ effect should be very surpressed, correct?
3. Finally, and just to confirm, does their work show that in a universe with a negative ω (and therefore an accelerated expansion caused by e.g. dark energy) the kSZ effect is enchanced (compared to a universe with ω=0, or no accelerated expansion) and therefore the photons are scattered, blueshifting them in the process?

 

[PeterDonis]

which would mean as far as I understand it that if Dark Energy was stronger or had a bigger density

Not a bigger density but a bigger tension (i.e., a pressure that is more negative). $w$ is the ratio of pressure to density; $w = -1$ means $p = - \rho$. $w < -1$ means $p < - \rho$, which is what is necessary to have a "Big Rip" scenario.

if ω was less negative than -1 (between 0 and -1) then that would be in a universe with a smalled dark energy density

No, a smaller tension. See above.

 

[PeterDonis]

If I understood it correctly, if ω was 0, there would be no accelerated expansion and therefore no dark energy of any form.

Actually, the threshold for accelerated expansion is $w < - 1/3$. The term "dark energy" would therefore only be warranted for that range of $w$. $w = 0$ is the value for cold matter (negligible pressure).

 

[PeterDonis]

in that case, the kSZ effect should be very surpressed, correct?

No. The kSZ effect does not require dark energy.

 

[PeterDonis]

does their work show that in a universe with a negative ω (and therefore an accelerated expansion caused by e.g. dark energy)

See the correction to this in post #3.

the kSZ effect is enchanced (compared to a universe with ω=0, or no accelerated expansion)

No. The "baseline" the paper is using is $w = -1$, which is the normal value for dark energy. And the paper is focused on analyzing only the dark energy-driven portion of the kSZ effect, which, per post #4, is not the total effect. So when the paper says "enhanced" or "suppressed", it only means the dark energy-driven portion of the effect relative to its "baseline" value at $w = -1$.

 

[Suekdccia]

See the correction to this in post #3.No. The "baseline" the paper is using is $w = -1$, which is the normal value for dark energy. And the paper is focused on analyzing only the dark energy-driven portion of the kSZ effect, which, per post #4, is not the total effect. So when the paper says "enhanced" or "suppressed", it only means the dark energy-driven portion of the effect relative to its "baseline" value at $w = -1$.

Mmmmh, but then, does it mean that the paper is saying that the part of the kSZ effect that is dependent on dark energy would be enhanced or surpressed depending on the value of ##w ? Then, if dark energy enhances it (at least in some part) wouldn't the total kSZ effect be a bit enhanced then?

 

[PeterDonis]

does it mean that the paper is saying that the part of the kSZ effect that is dependent on dark energy would be enhanced or surpressed depending on the value of ##w ?

Yes.

Then, if dark energy enhances it (at least in some part) wouldn't the total kSZ effect be a bit enhanced then?

Yes. But it seemed like you were overestimating the size of the dark energy effect.

 

[Suekdccia]

Yes.Yes. But it seemed like you were overestimating the size of the dark energy effect.

Perhaps I was explaining myself in a way that could be easily misunderstood.

One more question, if dark energy can enhance the kSZ effect by a bit, would it mean then that the photons would be a bit blueshifted as a consequence?

 

[PeterDonis]

if dark energy can enhance the kSZ effect by a bit, would it mean then that the photons would be a bit blueshifted as a consequence?

I believe that is what "enhance" means in the paper.

 

[Suekdccia]

I believe that is what "enhance" means in the paper.

Thank you

I asked a similar question in another forum and someone replied this:

The kSZ effect is the result of CMB photons undergoing inverse Compton scattering with fast moving electrons inside galaxy clusters. This happens regardless of whether there is dark energy or not.

It doesn't make sense to talk about red- and blue-shifting, since this is a scattering process what we measure is a distortion in the CMB spectrum away from a pure black-body one along lines of sight that intersect galaxy clusters. This results in localised fluctuations in the inferred CMB temperature. Where the paper talks about the effect being enhanced or suppressed, it is referring to the magnitude of these temperature fluctuations relative to the fiducial LCDM model.

Section 2 of the paper goes through the mathematics of calculating the "power spectrum" of the kSZ effect i.e. how the magnitude of the fluctuations varies with angular scale. This depends on the Hubble parameter H(z), which in turn depends on (among other things) the presence and nature of dark energy. The point of the paper is to investigate whether it's possible to work backwards from the measured kSZ power spectrum to constrain the properties of dark energy.

Their overall conclusion is best summarised by equations 19-22, which are fitting formulae that describe how the power spectrum changes for any combination of w_0 and w_a. Restricting to the case w_a=0, they find that the kSZ effect is enhanced for w_0 < -1 and suppressed for w_0 > -1.

Everything is fine, but I don't understand when he mentioned that it doesn't make sense to talk about blueshifting and redshifting. I mean, even if we are fluctuations in CMB temperature, wouldn't these fluctuations translate into blueshifting and redshifting?

 

[PeterDonis]

I don't understand when he mentioned that it doesn't make sense to talk about blueshifting and redshifting.

Any time you talk about blueshifting and redshifting, you are assuming some "baseline" frequency or wavelength that the shifts are relative to. For example, when we talk about cosmological redshifts in general, we are talking about redshifts of particular spectral lines, compared to what we observe in a laboratory on Earth.

"Temperature" of radiation is something different: it relates to the distribution of intensity as a function of frequency or wavelength. "Fluctuations in CMB temperature", strictly speaking, means intensity variations, not variations in frequency or wavelength. (Moreover, as your commenter in the other thread points out, these intensity variations mean that the overall CMB spectrum is no longer a black body spectrum--which also means that the concept of "temperature" no longer is strictly well defined, since strictly speaking it is only well defined for a black body spectrum. But that's a technicality that probably isn't relevant for this discussion.)

On the other hand, as your commenter also notes, the source of the kSZ effect is inverse Compton scattering, which, as any basic treatment will tell you, changes the frequency (and wavelength) of the light. In other words, a blueshift (or redshift in the case of ordinary Compton scattering as opposed to inverse). So the reason for the intensity fluctuations is ultimately that photons are being shifted in frequency, relative to the frequency they had before being scattered. So one can view that process as blueshifting or redshifting, even though it can also be viewed as temperature or intensity fluctuations.

All that said, the effect of dark energy on all this has nothing to do with inverse Compton scattering or anything like that. The effect of dark energy is just a form of cosmological redshift, i.e., due to the expansion of the universe, and affects all photons whether they are inverse Compton scattered or not. Roughly speaking, the dark energy equation of state affects the relationship between the overall cosmological redshift and the observed fluctuations due to the kSZ effect; that is what the paper you referenced in the OP is studying.

Note also that the observed redshift $z$ is a direct observable, so from that point of view thinking of dark energy as "blueshifting" or "redshifting" photons compared to what the kSZ effect would produce without any dark energy at all, is somewhat backwards. What we're really looking at is the relationship between observables: $z$ is one, the CMB intensity as a function of frequency is another, and the variation in CMB intensity with direction is still another. The exact dark energy equation of state affects those relationships. (Note, though, that this objection has nothing to do with what your commenter said in the other forum.)

 

[Suekdccia]

Note also that the observed redshift z is a direct observable, so from that point of view thinking of dark energy as "blueshifting" or "redshifting" photons compared to what the kSZ effect would produce without any dark energy at all, is somewhat backwards. What we're really looking at is the relationship between observables: z is one, the CMB intensity as a function of frequency is another, and the variation in CMB intensity with direction is still another. The exact dark energy equation of state affects those relationships. (Note, though, that this objection has nothing to do with what your commenter said in the other forum.)

Then is it actually incorrect to say that dsrk energy could enhance the blueshifting (at least in part)?

 

[PeterDonis]

Then is it actually incorrect to say that dsrk energy could enhance the blueshifting (at least in part)?

It depends on how you want to look at it.

 

[Suekdccia]

It depends on how you want to look at it.

Or at least we could say that dark energy enhances the blueshift indirectly?

 

[PeterDonis]

Or at least we could say that dark energy enhances the blueshift indirectly?

It depends on how you want to look at it.

 

[Suekdccia]

It depends on how you want to look at it.

I believe I'm having a bit of difficulty trying to understand this

 

[PeterDonis]

I believe I'm having a bit of difficulty trying to understand this

Then you need to read my post #11 more carefully. The point I have restated twice now is the main point of that post: that there are multiple ways to view what is going on, some of which involve "enhances the blueshift" and some of which don't.

 

[Suekdccia]

What we're really looking at is the relationship between observables: z is one, the CMB intensity as a function of frequency is another, and the variation in CMB intensity with direction is still another. The exact dark energy equation of state affects those relationships.

I think this is the part that is confusing me a bit, because if dark energy affects the relationship of all these elements, and CMB photons frequencies and their variation are part of this relations, it should follow that dark energy could cause a shift in their frequencies (e.g. blueshift)

 

[PeterDonis]

I think this is the part that is confusing me a bit, because if dark energy affects the relationship of all these elements, and CMB photons frequencies and their variation are part of this relations, it should follow that dark energy could cause a shift in their frequencies (e.g. blueshift)

Again, as I pointed out at the start of post #11, any talk of "blueshift" or "redshift" implies a "baseline" frequency that the shifts are relative to. What "baseline" are you using? Think carefully.

 

[Suekdccia]

Again, as I pointed out at the start of post #11, any talk of "blueshift" or "redshift" implies a "baseline" frequency that the shifts are relative to. What "baseline" are you using? Think carefully.

As far as I understand we would be using as a baseline the CMB frequency measured in a universe with w=-1. In the paper the authors say that in a universe with w=0 the effect should be supressed (redshifted) and for more negative pressure it should be enhanced (blueshifted). As dark energy affects the equation of state, it should then follow that more negative pressure results in a blueshift (at least in the case studied in the paper)

 

[PeterDonis]

we would be using as a baseline the CMB frequency measured in a universe with w=-1

There is no "CMB frequency". The CMB parameter we measure is intensity as a function of frequency and direction on the sky.

 

[Suekdccia]

There is no "CMB frequency". The CMB parameter we measure is intensity as a function of frequency and direction on the sky.

Which is related to the CMB temperature. Wouldn't this in turn be related to frequency and possible shifts?

 

[PeterDonis]

Which is related to the CMB temperature.

As I said in post #11, the CMB "temperature" is extracted from the intensity distribution by frequency based on known black body radiation properties. But the actual CMB, with all the fluctuations in it, is not an exact black body. So describing the fluctuations in intensity in different directions as temperature fluctuations is somewhat of a misnomer. It's a reasonable intuitive heuristic, but you have to be aware of its limitations.

Wouldn't this in turn be related to frequency and possible shifts?

We'd better take a step back at this point and walk through this from scratch.

First, let's look at an idealized CMB which is an exact black body with no fluctuations whatever; at any frequency, the observed intensity of the CMB is the same in all directions. (In other words, we are talking about an idealized CMB in a universe where the only thing that ever happens to CMB radiation is the cosmological redshift; no kSZ effect or anything else.) Then, as above, we can use known black body radiation properties to calculate a temperature for the CMB as we observe it today. We can then use known properties of ionization of hydrogen to calculate the temperature the CMB had when it was emitted. The ratio of those two temperatures gives us the cosmological redshift of the CMB; more precisely, $T_{\text{emitted}} / T_{\text{observed}} = 1 + z$, where $z$ is the CMB cosmological redshift. (Note that this also assumes that the cosmological redshift does not change the black body nature of the CMB radiation, which is what our best current model predicts.)

Next, let's suppose that the CMB radiation coming to us along one particular direction passes through some plasma that causes it to undergo inverse Compton scattering. (This is the kSZ effect.) The inverse Compton scattering blueshifts the CMB photons coming from that direction. If we assume that this blueshift does not change the black body nature of the radiation (which is actually not a good assumption, as I have mentioned before, but I'll leave that aside for this post), then we can view the blueshift as a shift upward in temperature, as compared to the CMB temperature in other directions. In other words, the CMB in that particular direction is observed to be slightly warmer than the CMB in other directions, because of the kSZ effect. As far as I can tell, this is what the paper means by the "kSZ signal".

(Note, btw, that the paper you referenced also talks about "reionization" as part of the kSZ effect. That is not something I'm familiar with and I'm not sure of the details of that part of it. I'm also not entirely clear about the specific mechanism of the dark energy effect that the paper discusses. So it's possible that I'm missing something relevant. I'm going to limit my analysis to what I think I have a reasonable grasp of.)

Now, what effect will the dark energy equation of state have on all this? While, as I noted just now, I'm not entirely clear on the details, as far as I can tell, when the paper talks about "enhancing" the kSZ effect, they mean that the temperature fluctuation--the "kSZ signal" described above--is larger than it would be at the "baseline" (which the paper appears to take to be the $w = -1$ dark energy equation of state), and when it talks about "suppressing" the kSZ effect, it means that the temperature fluctuation is smaller than it would be at the "baseline". However, note that this is not the same as looking at the effect as compared to what the kSZ signal would be with no dark energy at all. As far as I can tell, compared to the "no dark energy at all" case, the kSZ signal is larger over the entire range of dark energy equations of state considered in the paper. It's just not as much larger for less negative values of $w$, as for more negative values of $w$. But even with no dark energy at all, the kSZ effect is still there; the kSZ signal is not zero.