I haven't heard of any lensing based on filament structures, but the folks who do what is called "weak lensing" might have some statistical arguments that can correlate their results with the likely (or unlikely) presence of filaments.
However I have to say from reading the article it still seems to me this is not what they are doing. Could just be due to an oversimplification by the article.
Yeah, it's considered a minor detail that isn't important enough for the article.:-) If you're curious about the code, it was written by Volker Springel (one of the Virgo consortium members) and is called GADGET. (actually, the simulation they're talking about was run with version 2 of GADGET, which isn't yet publically available, but is similar to v1.1 which is on the GADGET webpage).
It seems to me they just said they were assigning a given energy level based on the amount of background radiation back at the point it started then iterating ( and using various shortcuts ) to then calculate each individual mass points affect on all 9,999,999,999 other mass points over time based on Keplers laws. In other words at its most basic it is a n-body simulation where n=10,000,000,000. Is it just over simplified ? That alone is a crapload of calculations, I would hate to have to figure out how to deal with a softening factor.
Setting the initial conditions is a little more complicated - they choose an input cosmological model, for which you can calculate the strength of density fluctuations as a function of size at early times (in this case, at t=340,000 years or so - we have a good idea of the fluctuation spectrum at that time because of the Cosmic Microwave Background), and then set up your initial conditions so that they contain the same spectrum of density fluctuations as the cosmological model you want to use.
But the force softening is actually quite easy to implement - instead of the force falling off as 1/r^2, as it would for a point mass, it's slightly weaker at small separations, depending on the exact density distribution of your "spheres". There are a few different choices you can make, but most people use a two-component spline that looks kind of like a Gaussian except that it goes to 0 exactly at 2 softening lengths.
It seems to me your saying this should create a system that acts similar to the universe while it is not supposed to be an exact model. Sort of like the chaos anaology with the drop of water.. no matter how precisely you drop it there is no real predicting how it will fall but you can make generelizations. Bigger the scale gets the more accurate your generalizations can get....
Yes, that's a great analogy.
However, considering the same forces are at work both in the planetary system and the universe at large why would you use the results from one method that could not also be used for the other?... A perfect understanding of gravity would allow a system of equations that would predict both pieces of information equally well I should think.
It's not the system of equations that's important here. The force law is the same - it's the details of the numerical integrator that are very different. Whenever you evolve a system with a finite timestep, there will be errors. Depending on what information you want, you can tolerate different levels of error. So, for example, if you want to know the positions of planets in a few thousand years, you need to minimize the error on the evolution of each individual particle in order to get an answer to the question you're asking.
In large simulations, the individual particles really represent some kind of smeared out density field. In fact, we "soften" the force law to take this into account - otherwise, when two particles get very close to each other, they receive huge gravitational kicks and fly far away from each other. This is unphysical - all that two particles very close to each other mean is that the density is very high there! So each "particle" really acts like a small sphere (densest at the center).
This also means that the spatial resolution of the simulation is the size of these spheres (known as the "softening length"). It is pointless to talk about positions much more precisely than the softening length. That means that you choose how large an error you're willing to accept from your numerical integrator by making sure that the difference in position between the answer you get and the "right" answer is a small fraction of the softening length.
Actually, there appears to be an error in the article, with the author leaving out a "*10^". 2^39 is supposed to be 2x10^39 and that is the number of zeros used in one of the excerpts(sp?). That works out to only 1E19 solar masses, significantly more than the mass of our galaxy by, oh, seven orders of magnitude.
As the AC below says, you're right that it should be 2x10^39, but that is equal to 10^9 solar masses, not 10^19 (1 solar mass = 2x10^30 kg)
No insult to all those who thought differently, but there is no resolution of galaxy parts in this simulation.
I'm sorry, but your math is wrong. Each particle is 10^9 solar masses, which is sufficient to reliably resolve halos down to 10^11 solar masses, roughly a factor of 10 smaller than the Milky Way.
Are they modeling any of the physical (star formation, etc) interactions of matter or just the gravitational interaction. It seemed like the latter, but the article did mention the apparent non-interaction of dark matter.
From the article:
The recently completed Millennium Run gave them the universe's broad distribution of matter as dictated by gravity. In upcoming simulations, other forces will come into play. Onto the web of matter the scientists will graft the electromagnetic aspects of normal matter, which by radiating photons allows gas to cool down and condense into spiral disks that originate stars. At the same time, hydrodynamic pressure, which ultimately derives from the fact that two atoms cannot overlap each other because of repulsion between their electrons, redistributes matter along the cosmic web's strands and nodes.
So this run is just gravity, but they will do more runs that include hydro, cooling, and presumably star formation. And to answer your first question
that works out to 100 to 200 data points to represent our galaxy. I wonder if they will get recognizeable spiral structures, etc?
Without hydro or cooling, all you get are ellipsoidal dark matter halos, no disks.
Further more they have to use some means of stabilizing the equations similar to solar system models which is a value based on observation but with no understanding for what really controls it ( if they don't do this then the system of equations can't model our own solar system much less 10 billion mass points expanding since 380k years after the big bang )
Actually, it doesn't work that way... we really don't care where each individual particle ends up, just what the overall phase space density is. The best way of thinking about it is as a Monte Carlo algorithm - the density and velocity fields of the original smoothly-distributed matter is sampled, and the evolution of each individual "particle" is such that the phase space densities that you reconstruct from the locations and velocities of all of the particles after the time step is the same as the actual phase space densities the real smooth matter distribution would have after that length of time (assuming the time step is short enough).
It's quite a different problem from solar system mechanics, where the particles represent real objects, in which case you really need to use a symplectic high-order integrator to make sure each individual particle is as close as possible to the right position and velocity.
(disclaimer: I Am An N-Body Modeller, and although I'm not part of the Virgo collaboration, a large fraction of what I do is study cosmological models like the one described)
It doesn't quite come out in the article, but what's really groundbreaking about this work is the number of particles they're using. When you make models like these, you always have to prioritize how large a volume you want to simulate (the more volume you have, the more representative a fraction of the universe you have and the larger number of structures you can analyze) vs how massive the particles are (the smaller the particles, the smaller structures you can analyze).
The more total particles you have, the less you need to compromise your volume or particle mass. Until now, simulating such a large a fraction of the universe (NOTE: unlike what the submitter said, this is not the full universe; as the article itself says, it's about 0.003 of the Hubble volume) required such large particles that it was impossible to say anything about individual galaxies.
However, with 10^10 particles, the mass of their particles is only about 10^9 solar masses, so they can reliably resolve structures of 10^11 solar masses. For reference, the mass of the Milky Way is roughly 10^12 solar masses. This is a fantastic leap forward - most other modern simulations have 10^8 - 10^9 particles, and so either can only simulate a much smaller fraction of the universe (like the simulations I study), or cannot say anything about galaxies, only massive galaxy clusters.
It's funny, this seems to fly in the face of the other articles we've seen on the settlement CDs which all seem to be complete worthless crap. There are a bunch of good CDs in that list (issues about whether the libraries are going to stock them aside).
As on offtopic aside, could they possibly have found a worse picture of Lou Reed for that CNN article?!
The more of you who don't read the full settlement, the more of it I get, since that $1 million is split evenly amongst everyone who fits into the class...
"We'll leave a jet-trail across the sky Just like Armstrong and the guys Vapour trail against the blue I'd get off on getting higher Is it over the Moon for the frequent flyer? Straight to the arms of...
Jezebel, I hear you well Or is it Gabriel? I can never tell
And the question's growing 'Cause it's not knowing When it's coming, where I'm going"
Funny, my reaction exactly matches what they said in the survey - it needs repairs more often than you'd hope (I've had to send it in twice in the three years I've had it), but the process of getting it repaired is as painless as humanly possible. Back within 48 hours the first time, 24 hours the second time!
Its the possibility of broad attenuation that I am wondering about, but lets leave this as an open question then since I have no concrete method to give you broad attenuation.
Just to follow up on CT's excellent response, it's worth mentioning that there is plenty of evidence for attenuation from dust in the universe, but not for "gray dust"... the attenuation is always wavelength-dependent. In the X-ray region, dust can block a lot of the soft (low-energy) X-rays, but doesn't do much blueward of 1-2 keV. So it's usually relatively easy to spot.
But even if there were a problem with dust, the amount of dust encountered along the line of sight increases monotonically with distance, so any effect that's due to dust will always have the same sign at all redshifts. What's interesting about this result (and also the newest supernova results), is that they see acceleration out to z~0.5, but deceleration beyond! That's exactly what you expect for a universe with 70% of the energy in a cosmological constant (or other dark energy with a similar equation of state) and inconsistent with any systematic effect (like dust) that anyone's thought up so far. Which doesn't mean that no one will, but for now the more likely interpretation is that the universe is dominated by something like a cosmological constant.
i got the impression neutrino's mass limit was too low really to be anywhere close to any % within the 95 %
That's true, but it's only very recently with the detection of two different sets of neutrino oscillations that there's finally a useful upper limit on the density of neutrinos in the universe, where "useful" means "can't be a significant fraction of the dark matter". 5 years ago we didn't know that for sure.
E=mc^2 doesn't mean that mass and energy are the same, it means that's the conversion you use when you convert between them. So if you could turn two 500nm photons into two massive particles (you can't turn a single photon into particles because of conservation of momentum), you could create two 4.4x10^-36 kg particles at rest in the center of mass frame.
It also means that photons do act as a source of gravity, with a strength equal to something with a mass of E/c^2. But in the current universe, their gravitational effect is tiny compared to the gravity of the mass... as a little exercise, try calculating the equivalent rest mass of the entire luminosity of the Milky Way and compare it to the mass of the moon.:-)
We understand the physics of brehmsstrahlung (the mechanism by which the X-rays are being emitted) quite well from experiments here on Earth. So it's straightforward to compute a temperature from the X-ray measurements and to understand how that relates to the luminosity.
What is less well known is whether the clusters are truly relaxed, which is key to relating the temperature and luminosity to the cluster mass (looking at the Chandra images, they certainly look relaxed... but there were clusters that looked relaxed on ROSAT images that Chandra resolved into quite clumpy-looking things). It also assumes that the only energy input into the X-ray emitting gas is gravitational; if supernova feedback or AGN (active galactic nuclei, like quasars and Seyfert galaxies) activity is important then that might change things. So those are the systematics to be worried about. However, there is not a single cluster where the X-ray emitting gas mass is not ~4 times smaller than the gravitational mass, so it's safe to say that a significant fraction of the cluster mass is dark.
I'm not entirely sure what your second sentence means, and I think you're confusing dark matter and dark energy, but I'm going to take a guess that you're talking about the former discrepancy between the ages of the oldest stars (calculated using calculations of stellar evolution) versus the age of the universe from cosmological observations. It used to be that the stars appeared to be older than the universe. But now that it appears that the universe is accelerating, that discrepancy has gone away - if the universe is accelerating now, that means it was expanding slower earlier and so took longer to expand to its current size.
As much as you don't want to hear that the current cosmological model has become standard because multiple pieces of evidence all point toward the it, it's true. It wouldn't have become standard otherwise. Dark energy fit the supernova observations, it fit the microwave background observations, it fits these X-ray observations, and it solves the age problem. The main problem now is that we don't know what it is. Hopefully we'll figure that out soon... if not, it will be because some other model will solve all those same problems AND other new ones such as the what-the-hell-is-it problem.
I would agree that the number does not change. The number of observable baryons will change over time as many of them end up inside black holes - which of course would constitue part of the dark matter.
The mass of black holes in a cluster is tiny compared to the mass of the X-ray emitting gas, which is the relevant number (that's what you're observing with Chandra).
Quick calculation: let's see each galaxy in the cluster has a 10^8 solar mass black hole (that's higher than average, but not absurd). There are maybe a thousand galaxies in one of these clusters (though most will be small galaxies that have smaller black holes), so the total black hole mass is no more than 10^11 solar masses. On the other hand, the total mass of the cluster is more like 10^14 solar masses. The baryon fraction is roughly 25%, so the baryonic mass of the cluster is around 2.5 x 10^13 solar masses and the fraction of that in black holes is less than 1%.
These clusters differ in age by 7 billion years. Is it really fair to assume the ratio of hot gas and other things is the same?
The ratio of baryons to dark matter isn't going to change. The questionable part of the assumptions are whether the clusters are truly relaxed (if not, the X-ray temperature may not match the total mass) and whether there is any additional energy input into the intracluster medium due to supernova feedback (if so, the X-ray temperature may not match the total mass).
Do cosmologists take into account the mass equivalent of all the non-dark energy (light) that is flying around in space? How about the radiation pressure from it?
Yes. At very high redshift, the energy density of radiation was higher than of matter... the crossover is around z=45,000 if I remember right. In the low-redshift (read: observable) part of the universe, the gravitational effect of radiation is negligible.
cassimir (sp?) effect on a galactic scale. Gravity from virtual particle pairs?
That's the best candidate for dark energy, which is exactly what they're measuring.;-)
Lastly, how does one calculate (as I read Feyman did) the energy density of free space? Link please.
clusters are filled with hot gas that emit X-rays with a spectrum indicative of their temperature (typically a million Kelvins or so)
the X-ray luminosity depends on the temperature and the gas mass
the temperature depends on the total (gas + dark) mass
Chandra measures the spectrum which gives you the temperature) and the flux (luminosity / distance^2)
therefore you can find the distance given the gas/dark mass ratio
because clusters are really big and sample a big fraction of the universe, the gas/dark mass ratio is typical of the universe as a whole... and more importantly, that means that all big clusters have the same gas/dark mass ratio
setting the gas/dark mass ratio of all 26 clusters equal gives you the ratio of all of their distances
measuring the redshift of the galaxies in the clusters gives you a relationship between the rate of expansion and distance (relative to the nearest cluster, say)
when you look at this diagram, you see that as things get farther away, the expansion rate increases... and then if you get really far away, it decreases again. this is exactly consistent with what you expect from the cosmological constant (or any form of dark energy with a similar equation of state)
Slashdot Mirror
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But the force softening is actually quite easy to implement - instead of the force falling off as 1/r^2, as it would for a point mass, it's slightly weaker at small separations, depending on the exact density distribution of your "spheres". There are a few different choices you can make, but most people use a two-component spline that looks kind of like a Gaussian except that it goes to 0 exactly at 2 softening lengths.
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It's not the system of equations that's important here. The force law is the same - it's the details of the numerical integrator that are very different. Whenever you evolve a system with a finite timestep, there will be errors. Depending on what information you want, you can tolerate different levels of error. So, for example, if you want to know the positions of planets in a few thousand years, you need to minimize the error on the evolution of each individual particle in order to get an answer to the question you're asking.
In large simulations, the individual particles really represent some kind of smeared out density field. In fact, we "soften" the force law to take this into account - otherwise, when two particles get very close to each other, they receive huge gravitational kicks and fly far away from each other. This is unphysical - all that two particles very close to each other mean is that the density is very high there! So each "particle" really acts like a small sphere (densest at the center).
This also means that the spatial resolution of the simulation is the size of these spheres (known as the "softening length"). It is pointless to talk about positions much more precisely than the softening length. That means that you choose how large an error you're willing to accept from your numerical integrator by making sure that the difference in position between the answer you get and the "right" answer is a small fraction of the softening length.
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Without hydro or cooling, all you get are ellipsoidal dark matter halos, no disks.
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It's quite a different problem from solar system mechanics, where the particles represent real objects, in which case you really need to use a symplectic high-order integrator to make sure each individual particle is as close as possible to the right position and velocity.
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(disclaimer: I Am An N-Body Modeller, and although I'm not part of the Virgo collaboration, a large fraction of what I do is study cosmological models like the one described)
It doesn't quite come out in the article, but what's really groundbreaking about this work is the number of particles they're using. When you make models like these, you always have to prioritize how large a volume you want to simulate (the more volume you have, the more representative a fraction of the universe you have and the larger number of structures you can analyze) vs how massive the particles are (the smaller the particles, the smaller structures you can analyze).
The more total particles you have, the less you need to compromise your volume or particle mass. Until now, simulating such a large a fraction of the universe (NOTE: unlike what the submitter said, this is not the full universe; as the article itself says, it's about 0.003 of the Hubble volume) required such large particles that it was impossible to say anything about individual galaxies.
However, with 10^10 particles, the mass of their particles is only about 10^9 solar masses, so they can reliably resolve structures of 10^11 solar masses. For reference, the mass of the Milky Way is roughly 10^12 solar masses. This is a fantastic leap forward - most other modern simulations have 10^8 - 10^9 particles, and so either can only simulate a much smaller fraction of the universe (like the simulations I study), or cannot say anything about galaxies, only massive galaxy clusters.
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How about if you could actually improve your overall productivity by slacking? ;-)
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It's funny, this seems to fly in the face of the other articles we've seen on the settlement CDs which all seem to be complete worthless crap. There are a bunch of good CDs in that list (issues about whether the libraries are going to stock them aside).
As on offtopic aside, could they possibly have found a worse picture of Lou Reed for that CNN article?!
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In Soviet Russia, repetitive joke overlords welcome you!
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I was thinking more along the lines of the first reactor meltdown... though it was more of a prototype than a full Candu design. ;-)
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Yes, please, believe that.
The more of you who don't read the full settlement, the more of it I get, since that $1 million is split evenly amongst everyone who fits into the class...
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Here's a full pre-print of the article.
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I suppose that's better than a Candu attitude. ;-)
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Here's your requisite 30%! ;-)
"We'll leave a jet-trail across the sky
Just like Armstrong and the guys
Vapour trail against the blue
I'd get off on getting higher
Is it over the Moon for the frequent flyer?
Straight to the arms of...
Jezebel, I hear you well
Or is it Gabriel? I can never tell
And the question's growing
'Cause it's not knowing
When it's coming, where I'm going"
-SOTW
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Funny, my reaction exactly matches what they said in the survey - it needs repairs more often than you'd hope (I've had to send it in twice in the three years I've had it), but the process of getting it repaired is as painless as humanly possible. Back within 48 hours the first time, 24 hours the second time!
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You obviously don't live in a city.
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But even if there were a problem with dust, the amount of dust encountered along the line of sight increases monotonically with distance, so any effect that's due to dust will always have the same sign at all redshifts. What's interesting about this result (and also the newest supernova results), is that they see acceleration out to z~0.5, but deceleration beyond! That's exactly what you expect for a universe with 70% of the energy in a cosmological constant (or other dark energy with a similar equation of state) and inconsistent with any systematic effect (like dust) that anyone's thought up so far. Which doesn't mean that no one will, but for now the more likely interpretation is that the universe is dominated by something like a cosmological constant.
That's true, but it's only very recently with the detection of two different sets of neutrino oscillations that there's finally a useful upper limit on the density of neutrinos in the universe, where "useful" means "can't be a significant fraction of the dark matter". 5 years ago we didn't know that for sure.
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E=mc^2 doesn't mean that mass and energy are the same, it means that's the conversion you use when you convert between them. So if you could turn two 500nm photons into two massive particles (you can't turn a single photon into particles because of conservation of momentum), you could create two 4.4x10^-36 kg particles at rest in the center of mass frame.
:-)
It also means that photons do act as a source of gravity, with a strength equal to something with a mass of E/c^2. But in the current universe, their gravitational effect is tiny compared to the gravity of the mass... as a little exercise, try calculating the equivalent rest mass of the entire luminosity of the Milky Way and compare it to the mass of the moon.
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"let's see" -> "let's say"
We understand the physics of brehmsstrahlung (the mechanism by which the X-rays are being emitted) quite well from experiments here on Earth. So it's straightforward to compute a temperature from the X-ray measurements and to understand how that relates to the luminosity.
What is less well known is whether the clusters are truly relaxed, which is key to relating the temperature and luminosity to the cluster mass (looking at the Chandra images, they certainly look relaxed... but there were clusters that looked relaxed on ROSAT images that Chandra resolved into quite clumpy-looking things). It also assumes that the only energy input into the X-ray emitting gas is gravitational; if supernova feedback or AGN (active galactic nuclei, like quasars and Seyfert galaxies) activity is important then that might change things. So those are the systematics to be worried about. However, there is not a single cluster where the X-ray emitting gas mass is not ~4 times smaller than the gravitational mass, so it's safe to say that a significant fraction of the cluster mass is dark.
I'm not entirely sure what your second sentence means, and I think you're confusing dark matter and dark energy, but I'm going to take a guess that you're talking about the former discrepancy between the ages of the oldest stars (calculated using calculations of stellar evolution) versus the age of the universe from cosmological observations. It used to be that the stars appeared to be older than the universe. But now that it appears that the universe is accelerating, that discrepancy has gone away - if the universe is accelerating now, that means it was expanding slower earlier and so took longer to expand to its current size.
As much as you don't want to hear that the current cosmological model has become standard because multiple pieces of evidence all point toward the it, it's true. It wouldn't have become standard otherwise. Dark energy fit the supernova observations, it fit the microwave background observations, it fits these X-ray observations, and it solves the age problem. The main problem now is that we don't know what it is. Hopefully we'll figure that out soon... if not, it will be because some other model will solve all those same problems AND other new ones such as the what-the-hell-is-it problem.
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Quick calculation: let's see each galaxy in the cluster has a 10^8 solar mass black hole (that's higher than average, but not absurd). There are maybe a thousand galaxies in one of these clusters (though most will be small galaxies that have smaller black holes), so the total black hole mass is no more than 10^11 solar masses. On the other hand, the total mass of the cluster is more like 10^14 solar masses. The baryon fraction is roughly 25%, so the baryonic mass of the cluster is around 2.5 x 10^13 solar masses and the fraction of that in black holes is less than 1%.
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Yes. At very high redshift, the energy density of radiation was higher than of matter... the crossover is around z=45,000 if I remember right. In the low-redshift (read: observable) part of the universe, the gravitational effect of radiation is negligible.
That's the best candidate for dark energy, which is exactly what they're measuring.
Weinberg, 1989. "The cosmological constant problem", Rev Mod Phys 61, 1 has a good summary.
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Here's a link to the article, which is accepted to MNRAS.
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Here's a quick summary of the technique:
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