[astroph/0509039] Local Pancake Defeats Axis of Evil
Authors:  Chris Vale 
Abstract:  Among the biggest surprises revealed by COBE and confirmed by WMAP measurements of the temperature anisotropy of the CMB are the anomalous features in the 2point angular correlation function on very large angular scales. In particular, the $\ell = 2$ quadrupole and $\ell = 3$ octopole terms are surprisingly planar and aligned with one another, which is highly unlikely for a statistically isotropic Gaussian random field, and the axis of the combined low$\ell$ signal is perpendicular to ecliptic plane and the plane defined by the dipole direction. Although this $< 0.1 %$ 3axis alignment might be explained as a statistical fluke, it is certainly an uncomfortable one, which has prompted numerous exotic explanations as well as the now well known ``Axis of Evil'' (AOE) nickname. Here, we present a novel explanation for the AOE as the result of weak lensing of the CMB dipole by local large scale structures in the local universe, and demonstrate that the effect is qualitatively correct and of a magnitude sufficient to fully explain the anomaly. 
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[astroph/0509039] Local Pancake Defeats Axis of Evil
This is an interesting paper that generated some discussion. It claims that a large part of the observed large scale CMB anisotropy may be due to lensing of a dipole, and hence help to explain some of the odd statistics observed in WMAP. The idea of explaining the anomalies by some local physics is certainly very appealing, and this paper seems more promising than previous attempts.
The local dipole we observe is of course not directly lensed as it is due to our local motion. However if the lensing matter is itself moving w.r.t. the CMB, then there can be an interesting dipole in the rest frame of the lens giving a nonzero contribution to the quadrupole and octopole. For this mechanism to work and give an interesting effect the lensing matter must be moving at a velocity comparable to our local velocity (lensing of the primordial dipole is a tiny effect assuming the primordial dipole has a sensible value; the dipole needs to be much larger than the primordial value).
The problem then seems to be the following: given that much of our local velocity may be due to infall into the Great Attractor and other local potential wells, is it reasonable to assume that the Great Attractor system doing the CMB lensing is moving w.r.t. the CMB fast enough to give an interesting effect?
The local dipole we observe is of course not directly lensed as it is due to our local motion. However if the lensing matter is itself moving w.r.t. the CMB, then there can be an interesting dipole in the rest frame of the lens giving a nonzero contribution to the quadrupole and octopole. For this mechanism to work and give an interesting effect the lensing matter must be moving at a velocity comparable to our local velocity (lensing of the primordial dipole is a tiny effect assuming the primordial dipole has a sensible value; the dipole needs to be much larger than the primordial value).
The problem then seems to be the following: given that much of our local velocity may be due to infall into the Great Attractor and other local potential wells, is it reasonable to assume that the Great Attractor system doing the CMB lensing is moving w.r.t. the CMB fast enough to give an interesting effect?

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[astroph/0509039] Local Pancake Defeats Axis of Evil
As we discussed offline I am not sure about this calculation. From what Chris writes in section 3 it looks like he is assuming that the mass simulating the great attractor is seeing the same dipole as we are, i.e. that it is at rest wrt the milky way.
However if our motion is driven mostly by the infall towards the great attractor then it would be safe to assume that the great attractor is close to at rest wrt the CMB frame. Therefore the dipole that is getting lensed would be much smaller than what he is lensing in his calculation.
in effect he is assuming that the lens is moving but I'm not sure that it is...
However if our motion is driven mostly by the infall towards the great attractor then it would be safe to assume that the great attractor is close to at rest wrt the CMB frame. Therefore the dipole that is getting lensed would be much smaller than what he is lensing in his calculation.
in effect he is assuming that the lens is moving but I'm not sure that it is...

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[astroph/0509039] Local Pancake Defeats Axis of Evil
These posts crossed with mine on the CMB Forum.
The paper claims that the gravitational lensing of the CMB dipole may indeed be modelled by a DM spherical mass [tex]M_{solar}^{17}[/tex] (~twice Great attractor) at a distance of 30 Mpc, however the paper also states that the effect may be modelled by smaller and closer masses, even by our own Galaxy if the DM halo is more massive and planar than expected.
It may well be reasonable to assume that these closer CMB lensing options are "moving w.r.t. the CMB fast enough to give an interesting effect"  especially if it is our own halo!
In my other post I also queried the confidence placed in the "age of precision cosmology" as the subsequent overestimation of the lowl power modes would cause problems in the WMAP analysis of other cosmological parameters.
Garth
The paper claims that the gravitational lensing of the CMB dipole may indeed be modelled by a DM spherical mass [tex]M_{solar}^{17}[/tex] (~twice Great attractor) at a distance of 30 Mpc, however the paper also states that the effect may be modelled by smaller and closer masses, even by our own Galaxy if the DM halo is more massive and planar than expected.
It may well be reasonable to assume that these closer CMB lensing options are "moving w.r.t. the CMB fast enough to give an interesting effect"  especially if it is our own halo!
In my other post I also queried the confidence placed in the "age of precision cosmology" as the subsequent overestimation of the lowl power modes would cause problems in the WMAP analysis of other cosmological parameters.
Garth

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[astroph/0509039] Local Pancake Defeats Axis of Evil
In the SZ simulations of the local universe (astroph/0505258, based on the constrained realization of astroph/0111099), the cluster Chris is talking about (A3627) has a kinetic SZ signal that is the opposite sign of that of Virgo. That would suggest that the dipole seen out there is quite different.

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[astroph/0509039] Local Pancake Defeats Axis of Evil
hi Gil. question is whether the magnitude of its velocity is big enough for the lensing of that local signal to give any relevant effect. presumably if they have calculated the kinetic SZE they have the exact velocity vector for the object.

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[astroph/0509039] Local Pancake Defeats Axis of Evil
The Nbody only (no gas) is available from the MPA site (http://www.mpagarching.mpg.de/galform/cr/index.shtml), so it would be straightforward to check. In fact, you could properly do the whole lensing operation with that box, presumably, and not have to use the "toy model" that Chris uses. Then the only question is whether the constrained realization is a good approximation to the local universe.
To clarify my thinking here: this effect has nothing to do with coherence, right? We should still see this effect even if we were at rest, and it is just a question of a moving gravitational lens. It looks like you get a differential redshift due to the object's motion along the line of sight when you are not in the flatsky limit. He chose the velocity along the line of sight relative to the CMB to be the same for the lens as for the MW, but the MW velocity doesn't affect the physics.
I think the important thing that simplifies the calculation is that he is in the lens rest frame. Using the constrained realization would probably require a different formalism, since the best rest frame to use would be the CMB frame and you would then have a whole bunch of lenses moving in all directions. There would no doubt be some cancellations due to + velocities, but you would also get transverse velocity effects.
To clarify my thinking here: this effect has nothing to do with coherence, right? We should still see this effect even if we were at rest, and it is just a question of a moving gravitational lens. It looks like you get a differential redshift due to the object's motion along the line of sight when you are not in the flatsky limit. He chose the velocity along the line of sight relative to the CMB to be the same for the lens as for the MW, but the MW velocity doesn't affect the physics.
I think the important thing that simplifies the calculation is that he is in the lens rest frame. Using the constrained realization would probably require a different formalism, since the best rest frame to use would be the CMB frame and you would then have a whole bunch of lenses moving in all directions. There would no doubt be some cancellations due to + velocities, but you would also get transverse velocity effects.

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[astroph/0509039] Local Pancake Defeats Axis of Evil
hmm...my point is that the lens (A3627) and the observer (MW) cannot be in the same rest frame since the MW is infalling. Assuming they do leads to assuming that the local dipole at the lens is the same as the one we observe. This means that you would over estimate the effect and its residual in the higher multipoles.

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[astroph/0509039] Local Pancake Defeats Axis of Evil
This is a clever idea to explain the alignment problem....
However seems to be not statistically favored even if lensing details you guys are discussing are resolved (unless I am misunderstanding
something). It requires a chance cancellation between the intrinsic
CMB (which is presumably gaussian random, and the quadrupole
being higher) and the anisotropy induced by the lensing effect.
This could be quantified but anyway nothing mysterious about that.
I *think* Chris assumed zero intrinsic CMB (at least in his plot) which
would perhaps be favored by a likelihood test, but then requires
postulating another mechanism to set the intrinsic CMB at these scales
to zero.
However seems to be not statistically favored even if lensing details you guys are discussing are resolved (unless I am misunderstanding
something). It requires a chance cancellation between the intrinsic
CMB (which is presumably gaussian random, and the quadrupole
being higher) and the anisotropy induced by the lensing effect.
This could be quantified but anyway nothing mysterious about that.
I *think* Chris assumed zero intrinsic CMB (at least in his plot) which
would perhaps be favored by a likelihood test, but then requires
postulating another mechanism to set the intrinsic CMB at these scales
to zero.

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[astroph/0509039] Local Pancake Defeats Axis of Evil
Hi guys
Lots of great input here, thanks. One thing I think I should have made more clear is just how uncertain the mass and velocity distribution in the local universe is; disagreements of order 1 and above are common in the observerational community, in part becasue much of the relevent structure is in the classic "zone of avoidance" behind the milky way, and also because of the usual issues involved in measuring photons and predicting mass. So, constrained simulations are great, but they're only as good as the constraints, and those are really uncertain. No reason not to try it, of course, but I don't know at the end whether you should believe the answer you wind up with.
On a second point, I think Dragan has picked up on something that I'd like to emphasize, which is that it would require a chance cancellation for lensing to both return the quadrupole to the level predicted in the standard model and eliminate the alignment issue. Not impossible, of course, but my feeling is that we have no reason to go the "coincidence" route. If anything, an *even lower* than current intrinsic quadrupole is what we would most likely have to face in the lensed dipole scenario, which would be an argument to go beyond the standard model, albeit not dramatically. For example, time evolution in w would do the trick, at least qualitatively, of lowering the quadrupole, but wouldn't mandate resorting to really odd universes that are shaped like donuts or whatever in order to handle the axis issue.
Chris
Lots of great input here, thanks. One thing I think I should have made more clear is just how uncertain the mass and velocity distribution in the local universe is; disagreements of order 1 and above are common in the observerational community, in part becasue much of the relevent structure is in the classic "zone of avoidance" behind the milky way, and also because of the usual issues involved in measuring photons and predicting mass. So, constrained simulations are great, but they're only as good as the constraints, and those are really uncertain. No reason not to try it, of course, but I don't know at the end whether you should believe the answer you wind up with.
On a second point, I think Dragan has picked up on something that I'd like to emphasize, which is that it would require a chance cancellation for lensing to both return the quadrupole to the level predicted in the standard model and eliminate the alignment issue. Not impossible, of course, but my feeling is that we have no reason to go the "coincidence" route. If anything, an *even lower* than current intrinsic quadrupole is what we would most likely have to face in the lensed dipole scenario, which would be an argument to go beyond the standard model, albeit not dramatically. For example, time evolution in w would do the trick, at least qualitatively, of lowering the quadrupole, but wouldn't mandate resorting to really odd universes that are shaped like donuts or whatever in order to handle the axis issue.
Chris

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[astroph/0509039] Local Pancake Defeats Axis of Evil
Chris,
In your paper you describe how the dipole lensing may be modelled by a 10^{17}M(solar) spherical mass at 30 Mpc, but that raises Antony's question: whether the "system doing the CMB lensing is moving w.r.t. the CMB fast enough to give an interesting effect?"
However in your paper you go on to say "nearby objects gain leverage, so that even our own Galaxy cannot be ruled out as a contributor if the dark matter halo is somewhat more massive and planar than expected."
As such closer objects might well be expected to be comoving with our frame of reference w.r.t. to the CMB this alternative lens may resolve Antony's objection. Have you any numbers on this option, e.g. could it be the Local Group intercluster DM?
Garth
In your paper you describe how the dipole lensing may be modelled by a 10^{17}M(solar) spherical mass at 30 Mpc, but that raises Antony's question: whether the "system doing the CMB lensing is moving w.r.t. the CMB fast enough to give an interesting effect?"
However in your paper you go on to say "nearby objects gain leverage, so that even our own Galaxy cannot be ruled out as a contributor if the dark matter halo is somewhat more massive and planar than expected."
As such closer objects might well be expected to be comoving with our frame of reference w.r.t. to the CMB this alternative lens may resolve Antony's objection. Have you any numbers on this option, e.g. could it be the Local Group intercluster DM?
Garth

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[astroph/0509039] Local Pancake Defeats Axis of Evil
I hesitate to get into the details of the local mass distribution (because I don't know much about it!), but I wouldn't rule out the Local Group or the Local Super Cluster as contributors. You can make up your own distributions as you like, just weight each object with Mass/Distance and compare to the toy model for point and planar distributions. For example, if the mass in the Local Group is centered between Andromeda and the Milky Way, you get about 10% of the toy effect if the LG has a mass of 10^14 M_sun and is distributed like a thick disk rather than a sphere. The same logic goes for the MW itself, which gives 10% if you can see it having a mass ~5.e12. And I think you need to weight with the velocity as well. e.g. the Earth is certainly not at rest w/r to the MW center, which I believe will actually give you a boost for these local structures.

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[astroph/0509039] Local Pancake Defeats Axis of Evil
I am still slightly confused over how does it work if lens and obsever are in different inertial systems. If observer is at rest wrt to CMB (assuming no intrinsic fluctuations) and lens alone is moving is observer seeing anything? In other words, does it help if you have a small mass moving very fast (i.e. faster than us) wrt to CMB? (I don't think so, but then why does the effect suddenly seems to depend on whether mass is at rest wrt to us or CMB?)
Also, as Dragan pointed out, you need chance aligment of intrinsic quadrupole and lensing effect to decrease the quadrupole amplitude as one would expect them to add in quadrature, making the low quadrupole anomaly stronger...
(btw  the title is great. More like an anime cartoon rather than a scientific paper...)
Also, as Dragan pointed out, you need chance aligment of intrinsic quadrupole and lensing effect to decrease the quadrupole amplitude as one would expect them to add in quadrature, making the low quadrupole anomaly stronger...
(btw  the title is great. More like an anime cartoon rather than a scientific paper...)

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Re: [astroph/0509039] Local Pancake Defeats Axis of Evil
Perhaps it is...Anze Slosar wrote:Also, as Dragan pointed out, you need chance aligment of intrinsic quadrupole and lensing effect to decrease the quadrupole amplitude as one would expect them to add in quadrature, making the low quadrupole anomaly stronger...
Garth

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[astroph/0509039] Local Pancake Defeats Axis of Evil
I also wrote a comment on this paper in my blog
http://atdotde.blogspot.com/2005/09/loc ... evil.html
however it's more on the analytical side of things.
http://atdotde.blogspot.com/2005/09/loc ... evil.html
however it's more on the analytical side of things.

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[astroph/0509039] Local Pancake Defeats Axis of Evil
Hi,
There was a question about how to do this calculation in the CMB rest frame and whether the effect would persist. The calculation turns out to be almost identical to the ISW calculation  the derivation is reasonably straightforward. To get the observed energy/temperarure you dot the photon 4momentum with the observer 4velocity. Working to O(v/c) always we have p=E(1,n) and u=(1,v_obs) so E_obs=E(1v_obs.n). Our motion induces a dipole.
So what is E? Starting with a photon initially of energy E_0 we solve the geodesic equation for p^\mu for a weak field. I find this easiest using the EulerLagrange equation in a metric with \Phi(xv_lens t) but however you do it one finds
dE/E = 2 v_lens.\nabla\Phi dt
Integrating the ith component rather than the 0th gives the bendangle formula  but this doesn't matter if you're lensing a monopole.
The integral is easiest to do if we assume the lens is spherical and centered on the observer, then you get the dipole you want I think. If the potential is compact and some distance away from you the effect is higher order. I suspect if you boost to the lens rest frame, lens the dipole and boost back you will also find a second order effect but I haven't verified this explicitly.
Martin.
There was a question about how to do this calculation in the CMB rest frame and whether the effect would persist. The calculation turns out to be almost identical to the ISW calculation  the derivation is reasonably straightforward. To get the observed energy/temperarure you dot the photon 4momentum with the observer 4velocity. Working to O(v/c) always we have p=E(1,n) and u=(1,v_obs) so E_obs=E(1v_obs.n). Our motion induces a dipole.
So what is E? Starting with a photon initially of energy E_0 we solve the geodesic equation for p^\mu for a weak field. I find this easiest using the EulerLagrange equation in a metric with \Phi(xv_lens t) but however you do it one finds
dE/E = 2 v_lens.\nabla\Phi dt
Integrating the ith component rather than the 0th gives the bendangle formula  but this doesn't matter if you're lensing a monopole.
The integral is easiest to do if we assume the lens is spherical and centered on the observer, then you get the dipole you want I think. If the potential is compact and some distance away from you the effect is higher order. I suspect if you boost to the lens rest frame, lens the dipole and boost back you will also find a second order effect but I haven't verified this explicitly.
Martin.