Does the Bullet Cluster Disprove MOND and Challenge ΛCDM?

[Earnest Guest]

I've read a lot of opinions and a lot of published pieces about the Bullet Cluster. Please correct me if I'm wrong, but the Bullet Cluster doesn’t prove ΛCDM (it has far too much collision velocity for such a model) so much as as it disproves MOND. The argument seems to be: MOND can describe galaxies pretty well and sort of describe galaxy clusters if you assume that most (>80%) of the mass is in the form of X-ray emitting gas. However, because the gravity lensing appears to follow the visible mass of the bullet cluster, then we can assume that gas doesn’t make up the majority of the mass of the cluster. Is this a fair statement of the argument?

Asked in a different way, what does it prove that the gravity lensing follows the visible mass and not the gas?

 

[Chalnoth]

Yes, I think that's fair. I'm not so sure the collision velocity of the Bullet Cluster is out of bounds with respect to $\Lambda$CDM, but I think that's a decent description of why MOND can't explain the Bullet Cluster. The closest I've seen to this is using a type of modified gravity model called tensor-vector-scalar gravity (TeVeS), but they still needed to make use of a new type of neutrino to make the fit work.

 

[Earnest Guest]

Yes, I think that's fair. I'm not so sure the collision velocity of the Bullet Cluster is out of bounds with respect to $\Lambda$CDM, but I think that's a decent description of why MOND can't explain the Bullet Cluster. The closest I've seen to this is using a type of modified gravity model called tensor-vector-scalar gravity (TeVeS), but they still needed to make use of a new type of neutrino to make the fit work.

Thanks. Can you (or anyone) take a stab at the last part: why is it significant that lensing follows the visible matter and not the gas?

 

[phyzguy]

This recent paper concludes that the Bullet Cluster is completely consistent with Lambda-CDM. In any model that attempts to explain dark matter by some modification of gravity, it's difficult to see how the different components can get separated. In Lambda-CDM, however, it is easy to see how the collisionless dark matter gets separated from the hot gas, which is influenced by pressure. As chalnoth said, the TeVeS folks attempted to explain the Bullet Cluster by saying that the collisionless galaxies get separated from the hot gas, and then the lensing of the galaxies is much stronger than GR would predict because the law of gravity is modified. But we can calculates how much mass is in the hot gas, and we know it is a lot more than in the galaxies, so why doesn't the hot gas lens even more strongly than the galaxies? It just doesn't add up. Lambda-CDM, however, appears to explain the observations quite well.

 

[phyzguy]

Thanks. Can you (or anyone) take a stab at the last part: why is it significant that lensing follows the visible matter and not the gas?

The lensing follows the dark matter, which is where most of the mass is. The dark matter and the galaxies are both collisionless, so they stay together. The gas is retarded by ram pressure as the two clusters pass through each other.

 

[Chalnoth]

Thanks. Can you (or anyone) take a stab at the last part: why is it significant that lensing follows the visible matter and not the gas?

The short answer is that MOND simply changes how gravity depends upon distance. The Bullet Cluster, however, shows the most gravitational attraction is not near where there is the most matter. No simple change in how gravity falls off with distance can possibly explain this.

Anyway, if you want a more in-depth explanation geared for a wide audience, check out this blog post:
http://www.preposterousuniverse.com/blog/2006/08/21/dark-matter-exists/

 

[Earnest Guest]

But we can calculates how much mass is in the hot gas, and we know it is a lot more than in the galaxies, so why doesn't the hot gas lens even more strongly than the galaxies?

I would greatly appreciate some ballpark estimates of the mass of the gas in the bullet cluster. All I've seen is people guessing at the Dark Halo mass so I'm confused about why they think there's so much to the mass in the gas part of the clusters. Even the report you cited seems to skip over that detail.

 

[Earnest Guest]

Anyway, if you want a more in-depth explanation geared for a wide audience, check out this blog post:
http://www.preposterousuniverse.com/blog/2006/08/21/dark-matter-exists/

Great post, but no references are given for the statement "It turns out that the large majority (about 90%) of ordinary matter in a cluster is not in the galaxies themselves, but in hot X-ray emitting intergalactic gas". This is news to me. Do you have any reading on the subject?

 

[phyzguy]

Table 1 of this paper has a detailed model for the total mass of the two clusters and the fraction of the total mass in the hot gas. The mass of the visible start in the galaxies is believed to account for only 1-2% of the total. The fraction of the mass in baryons is quite consistent with the prediction of Lambda-CDM, which says that about 16% of the total matter of the universe is baryons (note that this does not include dark energy).

 

[Earnest Guest]

Λ

Table 1 of this paper has a detailed model for the total mass of the two clusters and the fraction of the total mass in the hot gas. The mass of the visible start in the galaxies is believed to account for only 1-2% of the total. The fraction of the mass in baryons is quite consistent with the prediction of Lambda-CDM, which says that about 16% of the total matter of the universe is baryons (note that this does not include dark energy).

I'm sorry, but this paper talks about a ΛCDM simulation. The paper is arguing in a circle: we simulate a ΛCDM collision and, surprise, ΛCDM!
Do we have any actual evidence that didn't start with a conclusion?

 

[phyzguy]

Λ
I'm sorry, but this paper talks about a ΛCDM simulation. The paper is arguing in a circle: we simulate a ΛCDM collision and, surprise, ΛCDM!
Do we have any actual evidence that didn't start with a conclusion?

The claim is that the observations are consistent with Lambda-CDM. You assume Lambda-CDM, simulate the collision, and get results that are quantitatively consistent with the observations. How else would you approach the problem? You have to assume some model. Let me turn it around. Has anyone been able to make any other set of self-consistent assumptions and build a quantitative model that is consistent with the observations? The answer is emphatically no. Any other attempt that I have seen isn't even close. You have to remember also that Lambda-CDM explains a huge number of other observations. The fact the same model, with the same set of parameters explains so many observations is quite compelling, in my opinion.

 

[Earnest Guest]

Let me try this again. The Bullet Cluster is proof of ΛCDM because 90% of the baryonic mass is in the form of gas, yet the gravitational lensing appears to follow the 10% of the stellar mass. And we are convinced that 90% of the baryonic mass is in the form of gas because... (please insert a reference here that measures the mass of the superheated gas and doesn't assume ΛCDM to produce a model).

 

[phyzguy]

Let me try this again. The Bullet Cluster is proof of ΛCDM because 90% of the baryonic mass is in the form of gas, yet the gravitational lensing appears to follow the 10% of the stellar mass. And we are convinced that 90% of the baryonic mass is in the form of gas because... (please insert a reference here that measures the mass of the superheated gas and doesn't assume ΛCDM to produce a model).

OK, let me try again. Here is the logic:

(1) We assume that we understand elementary particle physics because we can measure protons, electrons, and atoms here on Earth and how much radiation they emit in certain circumstances. If you don't accept this, than we have no basis for a discussion.

(2) We assume that we understand stars, how much light they emit, and how much they weigh. Again, if you don't accept this, same comment as above.

(3) We measure how much X-ray radiation is emitted by the Bullet Cluster. From this we can calculate how much hot gas is present in the cluster, and where it is.

(4) From the brightness of the galaxy, we can calculate how much mass is present in stars.

(5) We measure the deflection of light that occurs by measuring the distortion of light from galaxies behind the Bullet Cluster. This is called gravitational lensing. From this, and the theory of General Relativity, we can calculate how much mass is present in the cluster. The theory of General Relativity has passed every experimental test that has been thrown at it, so we are highly confident it is correct. If you don't accept it, please propose an alternative theory that is at least as successful, quantitatively, at explaining the observations.

These calculations give the following results. About 15% of the total mass of the cluster is in hot gas; about 1-2% of the mass of the cluster is in stars; about 85% of the mass of the cluster is invisible, but we know it is there because it bends the light. This quantity of "dark" matter is very consistent with the amount that we get from measuring the CMB radiation, and from measuring galactic rotation curves, giving us some confidence that we have a model that makes sense.

 

[Earnest Guest]

It is step #3 that I'm having trouble following. PV = nRT. We can know the temperature, we can know the volume (roughly, it is, after all, a bow shaped shock wave). So how do you know what the pressure is? You need that to know the number of moles (the mass) of the cloud. If there is some other method available, I'd love to be educated about it.

 

[Chalnoth]

It is step #3 that I'm having trouble following. PV = nRT. We can know the temperature, we can know the volume (roughly, it is, after all, a bow shaped shock wave). So how do you know what the pressure is? You need that to know the number of moles (the mass) of the cloud. If there is some other method available, I'd love to be educated about it.

The two variables that are useful here are the temperature and luminosity. At a given temperature, each atom in the gas, on average, radiates a certain amount. So the total luminosity gives the total number of atoms.

 

[phyzguy]

The two variables that are useful here are the temperature and luminosity. At a given temperature, each atom in the gas, on average, radiates a certain amount. So the total luminosity gives the total number of atoms.

Exactly. The gas is very low density, and so it is transparent (optically thin). So we can basically see all of the atoms in the gas. For gas this hot, it is mostly the electrons that radiate, from a process called bremsstrahlung. From the total luminosity, we can calculate the total number of electrons in the gas. Since we know that for each electron there is a proton, we can calculate the total mass of the gas. There is a small correction depending on the exact composition of the gas ( it is mostly hydrogen, but there is some helium and a little bit of heavier elements), but this is a small correction for the level of accuracy we are talking about.

 

[Earnest Guest]

The two variables that are useful here are the temperature and luminosity. At a given temperature, each atom in the gas, on average, radiates a certain amount. So the total luminosity gives the total number of atoms.

Sorry, but I'm still missing the part where we set aside the Ideal Gas Law. Won't the same number of atoms glow twice as hot if the pressure is doubled?

 

[Chalnoth]

Sorry, but I'm still missing the part where we set aside the Ideal Gas Law. Won't the same number of atoms glow twice as hot if the pressure is doubled?

We measure the temperature directly by looking at the spectrum. Sure, if the pressure were to be changed, that would change the temperature, but we observe the temperature.

 

[Earnest Guest]

We measure the temperature directly by looking at the spectrum. Sure, if the pressure were to be changed, that would change the temperature, but we observe the temperature.

At some point, there must be an assumption of pressure. That's what I can't get my head around. If you double the pressure, you'll only need one-half of the same mass to make the same temperature appear in the sky, so how can the mass be related entirely on the surface density and volume?

 

[phyzguy]

At some point, there must be an assumption of pressure. That's what I can't get my head around. If you double the pressure, you'll only need one-half of the same mass to make the same temperature appear in the sky, so how can the mass be related entirely on the surface density and volume?

I'm not quite sure what you're missing. P = n k T, where n is the density per unit volume. As chalnoth said, we measure the temperature directly from the spectrum. The X-ray luminosity is a function of n and T, so by measuring the X-ray luminosity and knowing T, we can calculate n. So the pressure isn't a free variable. In fact, we measure n(r), where r is the distance tom the center of the cluster, because we know the luminosity as a function of r. Since we know n(r), we can calculate the total mass. What is the issue?
Maybe slide 2 from http://www2.astro.psu.edu/~caryl/a480/lecture12_10.pdf will help?

 

[Chalnoth]

At some point, there must be an assumption of pressure. That's what I can't get my head around. If you double the pressure, you'll only need one-half of the same mass to make the same temperature appear in the sky, so how can the mass be related entirely on the surface density and volume?

No, not at all. There's no reason to even use the ideal gas law, because we don't need to know either the pressure or the volume here. We can get the total brightness of the gas cloud by adding up the photons coming from the entire cluster. We can get the temperature of the gas by examining its spectrum. That's it. That's all we need to get the mass.

 

[Earnest Guest]

No, not at all. There's no reason to even use the ideal gas law, because we don't need to know either the pressure or the volume here. We can get the total brightness of the gas cloud by adding up the photons coming from the entire cluster. We can get the temperature of the gas by examining its spectrum. That's it. That's all we need to get the mass.

I'm sure that is the case. I know the Ideal Gas Law. I don't know the law that allow you to do what you are describing. Would you please give it a name and, if possible, a reference so I can read up on it.
Thanks!

 

[Earnest Guest]

I'm not quite sure what you're missing. P = n k T, where n is the density per unit volume. As chalnoth said, we measure the temperature directly from the spectrum. The X-ray luminosity is a function of n and T, so by measuring the X-ray luminosity and knowing T, we can calculate n. So the pressure isn't a free variable. In fact, we measure n(r), where r is the distance tom the center of the cluster, because we know the luminosity as a function of r. Since we know n(r), we can calculate the total mass. What is the issue?
Maybe slide 2 from http://www2.astro.psu.edu/~caryl/a480/lecture12_10.pdf will help?

Actually, the second slide did help, a lot.
First, you are incorrect about P = n k T having all the information you need. 'n' in the equation is the density which is just a refactoring of the V and the n parameters from the Ideal Gas Law. So P and n are still both unknowns even with the Boltzmann form of the gas law.
The missing piece is this: the gas in the cluster is assumed to be in hydrostatic equilibrium. So the pressure is:

{\frac{dP}{dr}}={\frac{GM(r)}{r^2}}\rho​

but, of course, this assumes that Newton's second law of motion is correct.

 

[PeterDonis]

n' in the equation is the density which is just a refactoring of the V and the n parameters from the Ideal Gas Law.

No, $n$ in this case is a direct observable; you can count the atoms by counting the photons they emit, and you can count the photons by knowing the temperature, which is the energy per photon, and the total luminosity, which is the total energy emitted.

this assumes that Newton's second law of motion is correct.

Do you have a reason for questioning that assumption? Bear in mind that we are talking about the non-relativistic regime, so the corrections to Newton's Laws due to GR are negligible.

 

[Earnest Guest]

No, $n$ in this case is a direct observable; you can count the atoms by counting the photons they emit, and you can count the photons by knowing the temperature, which is the energy per photon, and the total luminosity, which is the total energy emitted.

I thought the whole idea of this 'braking' radiation was that the gas was cooling (giving off radiation) while the pressure added energy back into the gas to keep it at equilibrium. How does the X-Ray emission stay constant if it's not under some pressure? Wouldn't it just cool down to the background radiation? And if it is under some pressure, how is that pressure not related to the temperature?

 

[Earnest Guest]

Do you have a reason for questioning that assumption?

Yes. Newton's Second Law clearly breaks down when trying to predict the velocity curves of galaxies (particularly LSB galaxies) and the Virial potential energy of galaxy clusters. Anyone who doesn't question the Second Law of Motion hasn't been paying attention.

 

[Chalnoth]

No, $n$ in this case is a direct observable; you can count the atoms by counting the photons they emit, and you can count the photons by knowing the temperature, which is the energy per photon, and the total luminosity, which is the total energy emitted.

Slightly pedantic, but not quite. The density isn't directly measured because we don't know the line of sight distance accurately. The total number is measured, so P and V are both unknowns.

I believe the assumption of hydrostatic equilibrium is a slightly different beast, used to determine the total gravitational mass of the cluster via the gas temperature:
https://ned.ipac.caltech.edu/level5/Sept01/Bahcall2/Bahcall3_4.html

 

[Chalnoth]

Yes. Newton's Second Law clearly breaks down when trying to predict the velocity curves of galaxies (particularly LSB galaxies) and the Virial potential energy of galaxy clusters. Anyone who doesn't question the Second Law of Motion hasn't been paying attention.

Presumably you mean Newtonian gravity isn't accurate? Attempts to modify gravity to explain astrophysical observations have failed.

 

[Earnest Guest]

Presumably you mean Newtonian gravity isn't accurate? Attempts to modify gravity to explain astrophysical observations have failed.

Don't put words in my mouth. I mean the Second Law of Motion isn't accurate. The failure of MOND is related to their attempt to fix gravity, which works just fine.

 

[Earnest Guest]

Slightly pedantic, but not quite. The density isn't directly measured because we don't know the line of sight distance accurately. The total number is measured, so P and V are both unknowns.

OK, so then (1) how do you calculate the pressure and (2) will doubling the pressure double the temperature?