[1101.1286] Discovery and Cosmological Implications of SPTCL J21065844, the Most Massive Known Cluster at z > 1
Authors:  R. J. Foley, K. Andersson, G. Bazin, T. de Haan, J. Ruel, P. A. R. Ade, K. A. Aird, R. Armstrong, M. L. N. Ashby, M. Bautz, B. A. Benson, L. E. Bleem, M. Bonamente, M. Brodwin, J. E. Carlstrom, C. L. Chang, A. Clocchiatti, T. M. Crawford, 
Abstract:  Using the South Pole Telescope (SPT), we have discovered the most massive known galaxy cluster at z > 1, SPTCL J21065844. In addition to producing a strong SunyaevZel'dovich effect signal, this system is a luminous Xray source and its numerous constituent galaxies display spatial and color clustering, all indicating the presence of a massive galaxy cluster. VLT and Magellan spectroscopy of 18 member galaxies shows that the cluster is at z = 1.132^+0.002_0.003. Chandra observations obtained through a combined HRCACIS GTO program reveal an Xray spectrum with an Fe K line redshifted by z = 1.18 +/ 0.03. These redshifts are consistent with galaxy colors in extensive optical, nearinfrared, and midinfrared imaging. SPTCL J21065844 displays extreme Xray properties for a cluster, having a coreexcluded temperature of kT = 11.0^+2.6_1.9 keV and a luminosity (within r_500) of L_X (0.5  2.0 keV) = (13.9 +/ 1.0) x 10^44 erg/s. The combined mass estimate from measurements of the SunyaevZel'dovich effect and Xray data is M_200 = (1.27 +/ 0.21) x 10^15 M_sun. The discovery of such a massive gravitationally collapsed system at high redshift provides an interesting laboratory for galaxy formation and evolution, and is a powerful probe of extreme perturbations of the primordial matter density field. We discuss the latter, determining that, under the assumption of LambdaCDM cosmology with only Gaussian perturbations, there is only a 7% chance of finding a galaxy cluster similar to SPTCL J21065844 in the 2500 deg^2 SPT survey region, and that only one such galaxy cluster is expected in the entire sky. 
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 Posts: 27
 Joined: September 25 2004
 Affiliation: University of Barcelona
[1101.1286] Discovery and Cosmological Implications of SPT
This paper looks at the detection of a large (>10^15) cluster at z~1.1 by the South Pole Telescope, and its cosmological implications. Sections 2 and 3 give a nice description of the detection and observational methods, but I’m a little concerned about section 4. One of the key claims of this work is that “there is a 7% chance of finding a cluster at least as massive and at a redshift at least as high”.
Quantifying the extreme nature of a single variable, such as mass, would be a meaningful frequentist statement (although for those evangelical Bayesians out there, no such statement exists, but bear with me…). I’m just a bit concerned by this double condition which is enforced – using both mass and redshift.
For example, take a sample population of people in the UK, only one person can claim to be the shortest, and one the heaviest. But many can claim that ‘no one is both shorter and heavier than me’. Perhaps each city has one such person. We don’t know how many of these people there will be, or their statistical significance, until we better understand the relationship linking the two variables. What is really needed is a single measure, such as BMI in this analogy.
An appropriate statistic needs to invoke the massz relationship, (as depicted in Fig 5 of 1101.1290), which then allows us to compute whether one cluster is more extreme than another. This analysis will likely generate a result significantly greater than the quoted 7%, as it opens up a much larger area of parameter space.
Quantifying the extreme nature of a single variable, such as mass, would be a meaningful frequentist statement (although for those evangelical Bayesians out there, no such statement exists, but bear with me…). I’m just a bit concerned by this double condition which is enforced – using both mass and redshift.
For example, take a sample population of people in the UK, only one person can claim to be the shortest, and one the heaviest. But many can claim that ‘no one is both shorter and heavier than me’. Perhaps each city has one such person. We don’t know how many of these people there will be, or their statistical significance, until we better understand the relationship linking the two variables. What is really needed is a single measure, such as BMI in this analogy.
An appropriate statistic needs to invoke the massz relationship, (as depicted in Fig 5 of 1101.1290), which then allows us to compute whether one cluster is more extreme than another. This analysis will likely generate a result significantly greater than the quoted 7%, as it opens up a much larger area of parameter space.

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[1101.1286] Discovery and Cosmological Implications of SPT
I guess I don't see the fundamental problem Fergus mentioned. After all, the upper bound predicted by a cosmological model (say bestfit LCDM) would, in this case, correspond to some curve in the [tex]M[/tex][tex]z[/tex] plane (for example, 95% curve or, to be more precise, curve bounding where 95% of LCDM models allowed by cosmological data contain 95% of their clusters). Whatever this curve shows, cluster or clusters above it can, given sufficient statistical significance, rule out LCDM. As mentioned in the previous post, this can happen in multiple ways, but that's fine.
This to me seems similar as comparing constraints from some new dataset to an old dataset in Ndimensional parameter space. The new set can be inconsistent with the old one in many different ways, with 'many' corresponding to different directions of nonoverlap of constraints in the parameter space. Moreover, multiple new datasets may all be inconsistent with the old data, in principle.
At any rate, these are interesting new papers by SPT. Too bad LCDM survives again.
This to me seems similar as comparing constraints from some new dataset to an old dataset in Ndimensional parameter space. The new set can be inconsistent with the old one in many different ways, with 'many' corresponding to different directions of nonoverlap of constraints in the parameter space. Moreover, multiple new datasets may all be inconsistent with the old data, in principle.
At any rate, these are interesting new papers by SPT. Too bad LCDM survives again.

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 Joined: September 25 2004
 Affiliation: University of Barcelona
[1101.1286] Discovery and Cosmological Implications of SPT
Hey Dragan,
I think this extreme example illustrates my concern:
Imagine everyone in the world has the same BMI. Now select one person at random.
No one is "shorter and heavier" than this person, in the whole world. So we have a remarkable 0% expectation of finding someone shorter and heavier when expanding our survey (or conducting our MCMC). Is this statistically significant? Have we found a special person? Certainly not, this same result arises for any individual, and it merely reflects the strong correlation which exists between height and mass.
But anyway, we're agreed that LCDM remains intact. And yes I certainly don't mean to detract from the importance of the SPT results.
I think this extreme example illustrates my concern:
Imagine everyone in the world has the same BMI. Now select one person at random.
No one is "shorter and heavier" than this person, in the whole world. So we have a remarkable 0% expectation of finding someone shorter and heavier when expanding our survey (or conducting our MCMC). Is this statistically significant? Have we found a special person? Certainly not, this same result arises for any individual, and it merely reflects the strong correlation which exists between height and mass.
But anyway, we're agreed that LCDM remains intact. And yes I certainly don't mean to detract from the importance of the SPT results.

 Posts: 27
 Joined: September 25 2004
 Affiliation: McGill University
[1101.1286] Discovery and Cosmological Implications of SPT
Hi Fergus,
What would you say is the best thing to use as a cluster mass index? Weight over height^2 obviously won't work. Number per dz and d(lnM) sort of does what you are talking about, but should this include the SPT selection function? If not, then you have to start worrying about stuff at reionization as possibly being there. A big advantage of >M,>z is it is easy to calculate, easy to explain.
From the results of the other SPT paper, you can guess that this object is not shockingly rare in a raw abundance sense: there are lower z objects that lightly stress LCDM by a comparable amount (setting aside that the Xray derived mass for this big one is a bit higher). If LCDM as a whole doesn't seem broken and there are 1 or 2 objects that are about as rare, then you know that this object can't be a huge outlier. However, even after saying all this, I am still amazed that something this big is sitting out at z>1 (I know, it borders on irrational).
What would you say is the best thing to use as a cluster mass index? Weight over height^2 obviously won't work. Number per dz and d(lnM) sort of does what you are talking about, but should this include the SPT selection function? If not, then you have to start worrying about stuff at reionization as possibly being there. A big advantage of >M,>z is it is easy to calculate, easy to explain.
From the results of the other SPT paper, you can guess that this object is not shockingly rare in a raw abundance sense: there are lower z objects that lightly stress LCDM by a comparable amount (setting aside that the Xray derived mass for this big one is a bit higher). If LCDM as a whole doesn't seem broken and there are 1 or 2 objects that are about as rare, then you know that this object can't be a huge outlier. However, even after saying all this, I am still amazed that something this big is sitting out at z>1 (I know, it borders on irrational).

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[1101.1286] Discovery and Cosmological Implications of SPT
To continue with Fergus' example, imagine a town with people with the same (or similar) BMI, where therefore 'every person is special' in having a more extreme (mass, 1/height^2) pair than anyone else.
Then the thing to do is compare these properties with theoretical prediction for the population of that size. That's the only comparison that matters. So for example, if by chance the theoretical model always predicts BMI[tex] \simeq [/tex]const with small uncertainty around this constant value, then there are two possible outcomes: either almost every person is an outlier, or almost nobody is. Then again, if the predicted BMI is variable (i.e. if the model predicts a relation in the (mass, height) with a slope different from 1/2 which is the BMI=const value), then only some (or a few) people may be unusual by the (mass, 1/height^2) criterion.
So even if we don't like the statistic for some subjective reason, it's the MonteCarlo comparison to theory that makes it fair. That's at least how I understand these approaches.
Then the thing to do is compare these properties with theoretical prediction for the population of that size. That's the only comparison that matters. So for example, if by chance the theoretical model always predicts BMI[tex] \simeq [/tex]const with small uncertainty around this constant value, then there are two possible outcomes: either almost every person is an outlier, or almost nobody is. Then again, if the predicted BMI is variable (i.e. if the model predicts a relation in the (mass, height) with a slope different from 1/2 which is the BMI=const value), then only some (or a few) people may be unusual by the (mass, 1/height^2) criterion.
So even if we don't like the statistic for some subjective reason, it's the MonteCarlo comparison to theory that makes it fair. That's at least how I understand these approaches.

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 Joined: September 25 2004
 Affiliation: University of Barcelona
Re: [1101.1286] Discovery and Cosmological Implications of
Hi Gil,
Yes it would be quite neat to define a 'Cluster Mass Index', m/f(z), but as you say, f(z) is not quite as simple as z^n! But since we have a natural reference "height" in this case, z=0, perhaps it would be informative to rescale masses to what we expect them to be at z=0. Looking at it this way, I wonder if SPTCL J21065844 is more massive (today) than any other known object?!Gil Holder wrote: What would you say is the best thing to use as a cluster mass index? Weight over height^2 obviously won't work. Number per dz and d(lnM) sort of does what you are talking about, but should this include the SPT selection function? If not, then you have to start worrying about stuff at reionization as possibly being there.
.
Ah, sorry I didn't mean to imply we should never perform this type of twoparameter cut, like p(m>M,z>Z). It only becomes pathological when, as in this example, the constants M and Z are defined after looking at the data. At least one of the two (ideally both) ought to be predefined. Otherwise we can get these rather nonsensical "every person is an outlier" scenarios! Or start worrying that last week's lottery numbers were a freak occurrence.Gil Holder wrote: A big advantage of >M,>z is it is easy to calculate, easy to explain.
.