Most AGN are variable, most likely due to hydrodynamic instabilities in the accretion disk around the black hole (it's easy to get instabilities if the disk is massive enough, since clumps can then grow through gravity, but I think you can also get some due to the interaction with the wind and/or photons coming from right at the black hole/inner edge of the accretion disk due to self-shielding effects).
While your point is well taken, I would argue that detection of dark matter via the gravitational interaction of stars and gas (as it was originally found) is qualitatively different enough from the detection of dark matter via gravitational lensing (as in the case of the Bullet cluster, and I suspect in this case - we'll find out soon) as to be non-circular.
The alternative to dark matter is that our theory of gravity is wrong, and different theories of gravity predict different amounts of gravitational lensing from the same configuration of matter. For example, the dynamics of galaxies in a galaxy cluster is (for all intents and purposes) the same in Newtonian gravity and in General Relativity, but the gravitational deflection of light from that cluster is different by a factor of 2. Therefore, a gravitational lensing detection of dark matter is an additional constraint over and above the dynamics of stars and gas.
Part of the confusion is that there are 2 separate concepts that both go by the name "dark matter".
Dark matter in the broad sense is matter that we detect gravitationally but can't observe directly through any interaction with light (and if this measurement is from gravitational lensing, which I suspect, then it certainly falls into this catagory). We infer that it exists because the motions of stars and gas in galaxies, galaxies and hot gas in galaxy clusters, and the universe as a whole all act as though they are acting in the gravitational field produced by much more mass than what we can directly detect.
Some fraction of this dark matter is normal ("baryonic") matter that just happens to be very difficult to detect due to its temperature and density... for example, a lot of it is diffuse gas at ~100000K, which is too cool to emit X-rays but too hot to emit much line radiation.
However, from Big Bang nucleosynthesis calculations, we can estimate how much baryonic matter there is in the universe because the relative fractions of different isotopes of H, He, Li and Be are quite sensitive to the total amount of baryonic matter. And the total amount of matter required to account for the dynamics of the universe is about 6 times higher than the amount of baryons that Big Bang nucleosynthesis measurements indicate.
Therefore, there must be non-baryonic dark matter too, made of exotic particles (or neutrinos, but there most likely aren't enough of those either). This is also sometimes just called "dark matter", which is confusing.
Interestingly, galaxy clusters, like the one studied here, have most of their baryonic matter in the form of hot X-ray gas that is detectable... the density of baryonic matter we can detect within a galaxy cluster is about what you'd expect given the BBN calculations. So any dark matter in a galaxy cluster should be non-baryonic dark matter, which is why measurements like this are exciting.
Given that the press conference isn't until May 15, I can't say for sure, but based on the brief blurb on the NASA website, it's almost certainly a gravitational lensing measurement.
It's true that dark matter doesn't interact directly with light, but it does curve space (ie. generate gravity), which light travels through. So light feels the gravitational effect of dark matter, a phenomenon known as "gravitational lensing". Essentially, the images of background galaxies going through a concentration of dark matter become magnified and distorted.
I don't know whether this is a strong lensing or weak lensing measurement. In strong lensing, the distortion is extreme and the images of the background get stretched into long tangential (and radial, though they're rarer) arcs like this. In the case of weak lensing, the distortion in any one image is small, but all images in a certain area are distorted coherently so you can statistically disentangle the signal.
Given the distorted images of the background galaxies, you can determine what mass distribution was responsible for those distortions, thereby producing a "mass map". It appears that in this case (again, based on the brief blurb), the mass map shows some sort of ring-like structure that isn't seen at any other wavelength (which non-dark matter would produce).
My sense is that the mass-dependent mass-to-light ratio that you get in a cosmological context does get you the right slope for the TFR. The zero-point is actually the bigger issue - simulated disk galaxies rotate too fast given their stellar mass. However, this may have finally been resolved by better treatments of how supernova energy feeds back on the surrounding gas - there's some recent work by Fabio Governato and collaborators that looks pretty encouraging (eg. Monthly Notices of the Royal Astronomical Society, 374, 1479).
For early-type galaxies, people usually use the Fundamental Plane rather than Faber-Jackson. The mass-to-light ratio has to vary with mass in a very interesting way to explain the curvature in the Fundamental Plane - it has to be high for low-mass dwarfs, low for L*-ish (ie. Milky Way sized) galaxies, and then high again for massive ellipticals and brightest cluster galaxies (see eg. Zaritsky et al. 2006, Astrophysical Journal, 638, 725). The physics at the high mass end is probably the same as the mass-to-light variation you need to explain the slope of the TFR, while at the low end there seems to be some process that inhibits stars from forming... it could be because most of the gas got heated by reionization, or that all the gas got blown out by supernovae, or it could be that star formation is just very inefficient in low-mass galaxies.
Originally TF was just a relationship between rotational speed and luminosity. Since luminosity is some measurement of stellar mass, it was proposed a few years ago that the true physical relationship was not with luminosity but with the total cooled baryonic mass (most of which is in the form of stars in most galaxies). So the Baryonic Tully Fisher relation was proposed, where they substituted the total mass of stars and gas instead of the luminosity. The relationship was tighter, indicating that this is closer to the fundamental relationship.
This work now takes it one more step and uses a more physical measurement for the other variable. Rotational speed of a disk galaxy tells you how deep the potential well is, assuming that all of the motion is in the form of rotation. But if there are also disordered motions, then it's really a combination of the disordered and ordered motion that tell you how deep the potential is. So they've replaced the rotation velocity with a combination of rotational velocity and velocity dispersion - and voila, the relationship is even tighter!
It's still a very bad idea. One of the uses of LSST data will be to co-add many images of the same piece of sky to detect fainter objects. For an object that produces one electron in a CCD pixel 20% of the time, the difference between "1" and "0" in those 20% of the images is crucial.
The problem that cold dark matter theorists have to deal with is that the extra-galactic dark matter can't just interact gravitationally, because gravity is too weak a force to produce structures in the short time the universe has been around. To clump in the manner observed, extra-galactic dark matter has to have some mechanism for losing energy. Otherwise two pieces of dark matter (or a piece of dark matter and a peice of ordinary matter) would just pass through each other. The dark matter would never be slowed down by anything, and so would never form clumps on any scale.
Actually, gravity on its own is easily enough to produce the structure we see. The dark matter doesn't dissipate any energy to form clumps, it simply falls toward the overdense regions, which become even more overdense because of all the infalling dark matter, ad infinitum. Each individual dark matter particle may pass right through all the other dark matter particles and go out the other side, but as long as it's moving at less than the escape speed then it turns around and comes back, bouncing around inside the clump forever.
In fact, one of the main problems now is that cold dark matter produces too many small clumps compared to the observations.
It's not so much that they assume what the universe should look like, as that they assume a particular property of the universe - that it's isotropic on large scales. Therefore, on average we view galaxies from a random angle and so the orientation of their images on the sky is random. You then look for statistical deviations in the orientations of the images due to lensing of the light by matter along the line of sight.
Isotropy is an assumption, but we have never detected a significant deviation from isotropy on large scales except for that due to effects that we expect - like the gravitational lensing that's used in this study.
But it's so simple. All I have to do is divine from what I know of Putin: is he the sort of man who would get the polonium-210 from his own nuclear reactor or his enemy's? Now, a clever man would get the polonium-210 from his own reactor, because he would know that only a great fool would put the evidence within reach. I am not a great fool, so clearly I can clearly not believe the evidence in Russia. But he must have known I was not a great fool, he would have counted on it, so I can clearly not believe the evidence in front of me.
Cute idea, but it doesn't work. Mass segregation only happens when the objects have many many many close interactions with their neighbours. They exchange energy in each interaction, and the equilibrium situation after many interactions is an equipartition of energy - each object has the same energy. Just looking at the kinetic energy, KE = m v^2, so a higher mass object has to have a lower velocity in order to have the same energy, which leads to mass segregation.
But you only reach equipartition after many interactions. Globular clusters are very dense, so that happens after a few billion years, but galaxies don't pass by each other very often (and when they do, they tend to merge more often than just get deflected), so you don't get a mass-segregated universe of galaxies (although you can to some degree in galaxy clusters which are more analagous to globular clusters).
What you're refering to is the "critical universe", which was what most astrophysicists used to believe we lived in because it's so much more elegant (and people had thought that it was a firm prediction of inflation because no one really thought that the cosmological constant wasn't zero). But it turns out that the universe is stranger...
(I already posted in this thread, otherwise I'd just mod parent up)
"Any non-standard gravitational force that scales with baryonic mass will fail to reproduce these observations." - Understand this statement, and you will understand why people now think that option 1 (dark matter) is more likely than option 2 (modified gravity)
Indeed! Just to elaborate so that more people will understand the statement:
There are lots of ways you could think of modifying gravity. In almost all of them, the strength of gravity from a blob of mass falls off with distance slightly differently than in GR. In the weak field ("Newtonian") limit, which is relevant on the scale of galaxies and galaxy clusters, that means that instead of going as 1/r^2 at all radii, gravity falls of as 1/r^2 until it gets sufficiently weak, at which point it transitions to something shallower like 1/r. But it still pulls matter towards it. In fact, any modification of GR that respects the equivalence principle must end up looking like this.
As long as gravity is modified in this way, the strength of the gravitational force from a distribution of matter can be different than what it would be for GR, but the direction can't.
What we have in this galaxy cluster is a measurement of the direction of gravitational attraction. And that doesn't point towards the baryons! So even for any modification of gravity that changes the scaling of gravity but doesn't change the direction, there must be dark matter.
Of course, that doesn't mean that dark matter is conclusively correct and modified gravity is conclusively wrong. But any sort of modified gravity that people have seriously considered can't explain these observations - you'd need to come up with much more baroque modifications. Whereas the existing dark matter theory actually predicted that you should see clusters exactly like this. So it's definitely the simpler explanation.
The main heating mechanism is simply that the gas is sitting in a very deep gravitational potential well, so in virial equilibrium the gas particles have to move very fast - ie. it must be several million Kelvin.
It's true that if that were the only thing going on there would be significant "cooling flows" in the clusters, but there's additional energy being pumped into the gas from the galaxies themselves, mostly in the form of jets from Active Galactic Nuclei/quasars (and, to a much lesser degree, supernovae). And in the case of this particular cluster, the merger of the two subclusters is shocking the gas and providing additional heating.
You're mistaking the data that is being clandestinely communicated (the password) and the data stream that it's being hidden in (an ssh/telnet session). The fact that the password is transmitted in one packet is independent of the packets of the ssh session in which that data is secretely transmitted.
What's interesting isn't the number. What's interesting is:
The technique of using detached binaries to measure distances can give accurate measurements for binary stars outside our galaxy. We'd always hoped to be able to do it, since it's a nice way of measuring distances that's independent of most other ways of doing it, but this is the first time it's actually been done. The fact that the number is even within 15% of previous results validates the technique.
If this is the correct distance scale and H0 is smaller, that reconciles some of the remaining differences regarding the fundamental parameters of cosmology that still existed between different types of exeriments (eg. those that measure fluctuations in the cosmic microwave background, clustering in galaxy redshift surveys, measurements of gravitational lensing) - the preferred value from other experiments has always been slightly smaller than the value that was measured directly. Therefore, it gives us more confidence in the validity of the physics used to describe the universe... which is the same physics we use here on Earth.
The fact that this distance is different from distances inferred from Cepheids and RR Lyrae means that there's something we don't understand about the structure and pulsation mechanisms in those stars. It's probably related to opacities of plasmas with different compisitions, something that's directly measurable here on earth and is an active area of research in fusion research (both civilian and military).
I'm not saying that you can directly point to a practical application of using detached binaries to measure the distance to M33. But it is an important part of understanding the universe, and the physics is relevant to things we do on Earth but is in a regime that is much harder to probe on Earth. Of course the number itself isn't the interesting part - saying that astronomers think it is and therefore their research is useless is a strawman.
Absolute measurements don't work nearly as well as relative measurements.
What they've done is compare the wavelengths at z=0 in the lab using one method and the wavelengths at z~2 in the quasar spectra using another method. They find an offset.
What would be much much more convincing is if they used one method both at low and high-z... for example, by comparing the low-z and high-z lines in the same spectrum. That's a true relative measurement, and would be be much better evidence.
...except that that's not at all what he's done. He's not adding any parameters at all, in fact... he's taken an existing model (TeVeS) that has a free function in it and constrained the form of the free function. So he's saying "if this other model is right, the function in it has to look something like this to fit the data".
Something you allude to here but deserves explicit reinforcement is that any workable alternative gravity theory (eg. TeVeS, BSTV) is at least as ad hoc as dark matter. At a minimum, any Lorentz-invarient alternative gravity theory requires an additional scalar field and an additional vector field (in the case of BSTV, 2 scalar fields and 1 vector field), with associated coupling constants as free parameters. The gravitational effect of dark matter depends almost entirely on its temperature and density. So this idea that alterating gravity is obviously more elegant than dark matter is a fallacy. Which isn't to say that it might not turn out to be right, but it's certainly not any more elegant.
Slashdot Mirror
Most AGN are variable, most likely due to hydrodynamic instabilities in the accretion disk around the black hole (it's easy to get instabilities if the disk is massive enough, since clumps can then grow through gravity, but I think you can also get some due to the interaction with the wind and/or photons coming from right at the black hole/inner edge of the accretion disk due to self-shielding effects).
[TMB]
...otherwise you'd be able to see brains through them.
[TMB]
While your point is well taken, I would argue that detection of dark matter via the gravitational interaction of stars and gas (as it was originally found) is qualitatively different enough from the detection of dark matter via gravitational lensing (as in the case of the Bullet cluster, and I suspect in this case - we'll find out soon) as to be non-circular.
The alternative to dark matter is that our theory of gravity is wrong, and different theories of gravity predict different amounts of gravitational lensing from the same configuration of matter. For example, the dynamics of galaxies in a galaxy cluster is (for all intents and purposes) the same in Newtonian gravity and in General Relativity, but the gravitational deflection of light from that cluster is different by a factor of 2. Therefore, a gravitational lensing detection of dark matter is an additional constraint over and above the dynamics of stars and gas.
[TMB]
Part of the confusion is that there are 2 separate concepts that both go by the name "dark matter".
Dark matter in the broad sense is matter that we detect gravitationally but can't observe directly through any interaction with light (and if this measurement is from gravitational lensing, which I suspect, then it certainly falls into this catagory). We infer that it exists because the motions of stars and gas in galaxies, galaxies and hot gas in galaxy clusters, and the universe as a whole all act as though they are acting in the gravitational field produced by much more mass than what we can directly detect.
Some fraction of this dark matter is normal ("baryonic") matter that just happens to be very difficult to detect due to its temperature and density... for example, a lot of it is diffuse gas at ~100000K, which is too cool to emit X-rays but too hot to emit much line radiation.
However, from Big Bang nucleosynthesis calculations, we can estimate how much baryonic matter there is in the universe because the relative fractions of different isotopes of H, He, Li and Be are quite sensitive to the total amount of baryonic matter. And the total amount of matter required to account for the dynamics of the universe is about 6 times higher than the amount of baryons that Big Bang nucleosynthesis measurements indicate.
Therefore, there must be non-baryonic dark matter too, made of exotic particles (or neutrinos, but there most likely aren't enough of those either). This is also sometimes just called "dark matter", which is confusing.
Interestingly, galaxy clusters, like the one studied here, have most of their baryonic matter in the form of hot X-ray gas that is detectable... the density of baryonic matter we can detect within a galaxy cluster is about what you'd expect given the BBN calculations. So any dark matter in a galaxy cluster should be non-baryonic dark matter, which is why measurements like this are exciting.
[TMB]
Given that the press conference isn't until May 15, I can't say for sure, but based on the brief blurb on the NASA website, it's almost certainly a gravitational lensing measurement.
It's true that dark matter doesn't interact directly with light, but it does curve space (ie. generate gravity), which light travels through. So light feels the gravitational effect of dark matter, a phenomenon known as "gravitational lensing". Essentially, the images of background galaxies going through a concentration of dark matter become magnified and distorted.
I don't know whether this is a strong lensing or weak lensing measurement. In strong lensing, the distortion is extreme and the images of the background get stretched into long tangential (and radial, though they're rarer) arcs like this. In the case of weak lensing, the distortion in any one image is small, but all images in a certain area are distorted coherently so you can statistically disentangle the signal.
Given the distorted images of the background galaxies, you can determine what mass distribution was responsible for those distortions, thereby producing a "mass map". It appears that in this case (again, based on the brief blurb), the mass map shows some sort of ring-like structure that isn't seen at any other wavelength (which non-dark matter would produce).
[TMB]
My sense is that the mass-dependent mass-to-light ratio that you get in a cosmological context does get you the right slope for the TFR. The zero-point is actually the bigger issue - simulated disk galaxies rotate too fast given their stellar mass. However, this may have finally been resolved by better treatments of how supernova energy feeds back on the surrounding gas - there's some recent work by Fabio Governato and collaborators that looks pretty encouraging (eg. Monthly Notices of the Royal Astronomical Society, 374, 1479).
For early-type galaxies, people usually use the Fundamental Plane rather than Faber-Jackson. The mass-to-light ratio has to vary with mass in a very interesting way to explain the curvature in the Fundamental Plane - it has to be high for low-mass dwarfs, low for L*-ish (ie. Milky Way sized) galaxies, and then high again for massive ellipticals and brightest cluster galaxies (see eg. Zaritsky et al. 2006, Astrophysical Journal, 638, 725). The physics at the high mass end is probably the same as the mass-to-light variation you need to explain the slope of the TFR, while at the low end there seems to be some process that inhibits stars from forming... it could be because most of the gas got heated by reionization, or that all the gas got blown out by supernovae, or it could be that star formation is just very inefficient in low-mass galaxies.
[TMB]
For those interested in more details, it looks like the preprint is available at http://arxiv.org/abs/astro-ph/0702643.
Originally TF was just a relationship between rotational speed and luminosity. Since luminosity is some measurement of stellar mass, it was proposed a few years ago that the true physical relationship was not with luminosity but with the total cooled baryonic mass (most of which is in the form of stars in most galaxies). So the Baryonic Tully Fisher relation was proposed, where they substituted the total mass of stars and gas instead of the luminosity. The relationship was tighter, indicating that this is closer to the fundamental relationship.
This work now takes it one more step and uses a more physical measurement for the other variable. Rotational speed of a disk galaxy tells you how deep the potential well is, assuming that all of the motion is in the form of rotation. But if there are also disordered motions, then it's really a combination of the disordered and ordered motion that tell you how deep the potential is. So they've replaced the rotation velocity with a combination of rotational velocity and velocity dispersion - and voila, the relationship is even tighter!
Very nice work.
[TMB]
It's still a very bad idea. One of the uses of LSST data will be to co-add many images of the same piece of sky to detect fainter objects. For an object that produces one electron in a CCD pixel 20% of the time, the difference between "1" and "0" in those 20% of the images is crucial.
[TMB]
In fact, one of the main problems now is that cold dark matter produces too many small clumps compared to the observations.
[TMB]
It's not so much that they assume what the universe should look like, as that they assume a particular property of the universe - that it's isotropic on large scales. Therefore, on average we view galaxies from a random angle and so the orientation of their images on the sky is random. You then look for statistical deviations in the orientations of the images due to lensing of the light by matter along the line of sight.
Isotropy is an assumption, but we have never detected a significant deviation from isotropy on large scales except for that due to effects that we expect - like the gravitational lensing that's used in this study.
[TMB]
But it's so simple. All I have to do is divine from what I know of Putin: is he the sort of man who would get the polonium-210 from his own nuclear reactor or his enemy's? Now, a clever man would get the polonium-210 from his own reactor, because he would know that only a great fool would put the evidence within reach. I am not a great fool, so clearly I can clearly not believe the evidence in Russia. But he must have known I was not a great fool, he would have counted on it, so I can clearly not believe the evidence in front of me.
[TMB]
Cute idea, but it doesn't work. Mass segregation only happens when the objects have many many many close interactions with their neighbours. They exchange energy in each interaction, and the equilibrium situation after many interactions is an equipartition of energy - each object has the same energy. Just looking at the kinetic energy, KE = m v^2, so a higher mass object has to have a lower velocity in order to have the same energy, which leads to mass segregation.
But you only reach equipartition after many interactions. Globular clusters are very dense, so that happens after a few billion years, but galaxies don't pass by each other very often (and when they do, they tend to merge more often than just get deflected), so you don't get a mass-segregated universe of galaxies (although you can to some degree in galaxy clusters which are more analagous to globular clusters).
[TMB]
What you're refering to is the "critical universe", which was what most astrophysicists used to believe we lived in because it's so much more elegant (and people had thought that it was a firm prediction of inflation because no one really thought that the cosmological constant wasn't zero). But it turns out that the universe is stranger...
[TMB]
The stars orbiting around the centre of mass of the system is "the stars interact[ing] with one another".
[TMB]
[TMB]
Oh to have mod points right now... :) Someone mod parent up!
[TMB]
Indeed! Just to elaborate so that more people will understand the statement:
There are lots of ways you could think of modifying gravity. In almost all of them, the strength of gravity from a blob of mass falls off with distance slightly differently than in GR. In the weak field ("Newtonian") limit, which is relevant on the scale of galaxies and galaxy clusters, that means that instead of going as 1/r^2 at all radii, gravity falls of as 1/r^2 until it gets sufficiently weak, at which point it transitions to something shallower like 1/r. But it still pulls matter towards it. In fact, any modification of GR that respects the equivalence principle must end up looking like this.
As long as gravity is modified in this way, the strength of the gravitational force from a distribution of matter can be different than what it would be for GR, but the direction can't.
What we have in this galaxy cluster is a measurement of the direction of gravitational attraction. And that doesn't point towards the baryons! So even for any modification of gravity that changes the scaling of gravity but doesn't change the direction, there must be dark matter.
Of course, that doesn't mean that dark matter is conclusively correct and modified gravity is conclusively wrong. But any sort of modified gravity that people have seriously considered can't explain these observations - you'd need to come up with much more baroque modifications. Whereas the existing dark matter theory actually predicted that you should see clusters exactly like this. So it's definitely the simpler explanation.
[TMB]
EM attraction is not a logical conclusion. It's energetically impossible to create regions of net charge at astronomical length scales.
[TMB]
The main heating mechanism is simply that the gas is sitting in a very deep gravitational potential well, so in virial equilibrium the gas particles have to move very fast - ie. it must be several million Kelvin.
It's true that if that were the only thing going on there would be significant "cooling flows" in the clusters, but there's additional energy being pumped into the gas from the galaxies themselves, mostly in the form of jets from Active Galactic Nuclei/quasars (and, to a much lesser degree, supernovae). And in the case of this particular cluster, the merger of the two subclusters is shocking the gas and providing additional heating.
[TMB]
You're mistaking the data that is being clandestinely communicated (the password) and the data stream that it's being hidden in (an ssh/telnet session). The fact that the password is transmitted in one packet is independent of the packets of the ssh session in which that data is secretely transmitted.
[TMB]
- The technique of using detached binaries to measure distances can give accurate measurements for binary stars outside our galaxy. We'd always hoped to be able to do it, since it's a nice way of measuring distances that's independent of most other ways of doing it, but this is the first time it's actually been done. The fact that the number is even within 15% of previous results validates the technique.
- If this is the correct distance scale and H0 is smaller, that reconciles some of the remaining differences regarding the fundamental parameters of cosmology that still existed between different types of exeriments (eg. those that measure fluctuations in the cosmic microwave background, clustering in galaxy redshift surveys, measurements of gravitational lensing) - the preferred value from other experiments has always been slightly smaller than the value that was measured directly. Therefore, it gives us more confidence in the validity of the physics used to describe the universe... which is the same physics we use here on Earth.
- The fact that this distance is different from distances inferred from Cepheids and RR Lyrae means that there's something we don't understand about the structure and pulsation mechanisms in those stars. It's probably related to opacities of plasmas with different compisitions, something that's directly measurable here on earth and is an active area of research in fusion research (both civilian and military).
I'm not saying that you can directly point to a practical application of using detached binaries to measure the distance to M33. But it is an important part of understanding the universe, and the physics is relevant to things we do on Earth but is in a regime that is much harder to probe on Earth. Of course the number itself isn't the interesting part - saying that astronomers think it is and therefore their research is useless is a strawman.[TMB]
Absolute measurements don't work nearly as well as relative measurements.
What they've done is compare the wavelengths at z=0 in the lab using one method and the wavelengths at z~2 in the quasar spectra using another method. They find an offset.
What would be much much more convincing is if they used one method both at low and high-z... for example, by comparing the low-z and high-z lines in the same spectrum. That's a true relative measurement, and would be be much better evidence.
[TMB]
GMOS is not the name of the telescope. The telescope is Gemini South. The spectrograph is GMOS (Gemini Multi Object Spectrograph).
[TMB]
...except that that's not at all what he's done. He's not adding any parameters at all, in fact... he's taken an existing model (TeVeS) that has a free function in it and constrained the form of the free function. So he's saying "if this other model is right, the function in it has to look something like this to fit the data".
[TMB]
Something you allude to here but deserves explicit reinforcement is that any workable alternative gravity theory (eg. TeVeS, BSTV) is at least as ad hoc as dark matter. At a minimum, any Lorentz-invarient alternative gravity theory requires an additional scalar field and an additional vector field (in the case of BSTV, 2 scalar fields and 1 vector field), with associated coupling constants as free parameters. The gravitational effect of dark matter depends almost entirely on its temperature and density. So this idea that alterating gravity is obviously more elegant than dark matter is a fallacy. Which isn't to say that it might not turn out to be right, but it's certainly not any more elegant.
[TMB]