[astro-ph/0311381] The XMM--NEWTON Omega Project: II.Cosmological implications from the high redshift L-T relation of X-ray clusters

Authors:  S. C. Vauclair, A. Blanchard, R. Sadat, J.G. Bartlett, J.-P. Bernard, M. Boer, M. Giard, D. H. Lumb, P. Marty, J. Nevalainen
Abstract:  The evolution with redshift of the temperature-luminosity relation of X-ray galaxy clusters is a key ingredient to break degeneracies in the interpretation of X-ray clusters redshift number counts. We therefore take advantage of the recent measurements of the temperature-luminosity relation of distant clusters observed with XMM-Newton and Chandra satellites to examine theoretical number counts expected for different available X-rays cluster samples, namely the RDCS, EMSS, SHARC, 160deg^2 and the MACS at redshift greater than 0.3. We derive these counts without any adjustment, using models previously normalized to the local temperature distribution function and to the high-z (z = 0.33) TDF. We find that these models having Omega_M in the range [0.85-1.] predict counts in remarkable agreement with the observed counts in the different samples. We illustrate that this conclusion is weakly sensitive to the various ingredients of the modeling. Therefore number counts provide a robust evidence of an evolving population. A realistic flat low density model (Omega_M = 0.3), normalized to the local abundance of clusters is found to overproduce cluster abundance at high redshift (above z = 0.5) by nearly an order of magnitude. This result is in conflict with the popular concordance model. The conflict could indicate a deviation from the expected scaling of the M-T relation with redshift.
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Syksy Rasanen
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[astro-ph/0311381] The XMM--NEWTON Omega Project: II.Cosmolo

Post by Syksy Rasanen » July 16 2005

Talking about Einstein-de Sitter... This paper claims that observations of cluster counts prefer a high \Omega_m as opposed to \Lambda plus low \Omega_m (no statistical significance is given), and that this conclusion is consistent with all previous analyses of X-ray selected samples performed with the same methodology.

Can someone who knows about clusters enlighten me as to what is the general opinion in the field about this? Is there something clearly wrong with these results, do other analyses lead to different conclusions, is there controversy?

Boud Roukema
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[astro-ph/0311381] The XMM--NEWTON Omega Project: II.Cosmolo

Post by Boud Roukema » August 26 2005

Syksy Rasanen wrote:Talking about Einstein-de Sitter... This paper claims that observations of cluster counts prefer a high \Omega_m as opposed to \Lambda plus low \Omega_m (no statistical significance is given), and that this conclusion is consistent with all previous analyses of X-ray selected samples performed with the same methodology.

Can someone who knows about clusters enlighten me as to what is the general opinion in the field about this? Is there something clearly wrong with these results, do other analyses lead to different conclusions, is there controversy?
Well, on this particular paper, i'll quote my own response in our internal Toruń cosmology group:
http://cosmo.torun.pl/pipermail/cosmo-t ... 00180.html

"Omega_matter = 1 (was Re: gas question)"
http://www.astro.uni.torun.pl/sympa/sha ... 00005.html

The article by Blanchard et al:
http://arxiv.org/abs/astro-ph/0311381

Look carefully at the figures. The triple-dotted-dashed line is the
model for an (Om_m=0.3, Om_Lambda=0.7). It's hard to find, but once you
find it, you'll see it matches the observations very, very nicely.

According to the authors, this triple-dotted-dashed line is for eq.~(6),
which replaces eq.~(2). The difference between the dtwo eqns is a factor
of (1+z).

The authors' derivation of eq.~(2), in other papers, obtains this (1+z)
factor from the density of the Universe at the time that the cluster
virialises. So unless you throw out rho = rho_0 (1+z)^3 , it's hard
to change the derivation.

However, if you just look at another derivation of the equivalent of
eq.~(2), i.e. a T-M relation, and look at the z evolution of,
e.g. equation (73) of

Niayesh Afshordi, Renyue Cen
http://arxiv.org/abs/astro-ph/0105020

then the (1+z) factor becomes essentially (1+ not much) over the
relevant redshift range.

In other words, Blanchard et al's figures, with Afshordi & Cen's
version of the T-M relation, give the concordance model.

Again in simpler words, Blanchard et al think that clusters form
in one way, Afshordi & Cen think they form in a somewhat different way,
leading to moderately different T-M relations and hence totally different
local curvature parameter inferences.

It's good to have dissidents around :). Sometimes they're right, sometimes they're wrong.

In answer to your question: do Afshordi & Cen better understand the T-M relation than Blanchard et al? This I don't know, my physical intuition here is lacking.

BTW: Alain Blanchard, at least, is continuing to defend this claim:

astro-ph/0502220

astro-ph/0503426

Niayesh Afshordi
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[astro-ph/0311381] The XMM--NEWTON Omega Project: II.Cosmolo

Post by Niayesh Afshordi » August 29 2005

While I'm humbled by the reference, I think the cluster community is well aware of the cosmology dependence of the T-M relation. I should say that I'm surprised why nobody else has noticed the obvious mistake. In fact, I brought up this very issue at the talk by Vauclair (I think) in an X-ray meeting in Maryland in January of 2004. Then, Alexei Vikhlinin noted that the evolution of T-M relation depends on how one defines the mass, i.e. in constant overdensity with respect to avergae OR critical density of the universe. Apparently, the 1+z evolultion is almost correct with the former definition of mass, while the latter definition (which is what I used in Afshordi & Cen 2001), evolves as H^{2/3}.

Well, I just checked the Vauclair et al. paper and if you look at Eq. 2, you'll notice that for a fixed overdensity with respect to the critical density, the expression in the paranthesis is constant, implying that the T-M relation evolves as 1+z independent of cosmology.

Therefore, it seems as if Vaculair et al. have used the wrong evolution.

Alain Blanchard
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Re: [astro-ph/0311381] The XMM--NEWTON Omega Project: II.Cos

Post by Alain Blanchard » January 31 2006

Niayesh Afshordi wrote:While I'm humbled by the reference, I think the cluster community is well aware of the cosmology dependence of the T-M relation. I should say that I'm surprised why nobody else has noticed the obvious mistake. In fact, I brought up this very issue at the talk by Vauclair (I think) in an X-ray meeting in Maryland in January of 2004. Then, Alexei Vikhlinin noted that the evolution of T-M relation depends on how one defines the mass, i.e. in constant overdensity with respect to avergae OR critical density of the universe. Apparently, the 1+z evolultion is almost correct with the former definition of mass, while the latter definition (which is what I used in Afshordi & Cen 2001), evolves as H^{2/3}.

Well, I just checked the Vauclair et al. paper and if you look at Eq. 2, you'll notice that for a fixed overdensity with respect to the critical density, the expression in the paranthesis is constant, implying that the T-M relation evolves as 1+z independent of cosmology.

Therefore, it seems as if Vaculair et al. have used the wrong evolution.
I do not think that we did the "obvious mistake".

Obviously the evolution of the M-T relation depends on which way is used to define the mass
(...)

if ones want to work on number counts one uses analytical expressions of the mass function N(M) like Jenkins et al. and similar stuff.
So In Vauclair et al. we used the definition of mass in M-T corresponding to the one used in N(M): that is we used "Virial mass" . This is the methodology which has been followed by us in the various works (Oukbir et al) but also by other works like Borgani et al. Eke etal. Henry et al.

We empahasized that we could get the concordance in agreement with the counts my modifying the scaling of the M-T relation, which would imply non gravitational physics in clusters, but not just by changing the definition...

I hope this helps to clarify!


Alain Blanchard

Niayesh Afshordi
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[astro-ph/0311381] The XMM--NEWTON Omega Project: II.Cosmolo

Post by Niayesh Afshordi » February 07 2006

I stand by my previous statement.

The theoretical statement that we prove in Afshordi & Cen 2001 is that, in the absence of non-gravitational heating , T \propto (HM)^{2/3}, if mass is measured within a fixed overdensity with respect to the critical density of the universe.

However, if we fix overdensity with respect to the critical density, i.e. \Omega_M \Delta(z,\Omega_M) = const., Eq. (2) in Vauclair et al. implies that T \propto (1+z) M^{2/3}, which is inconsistent with above theoretical expectation for \Lambda CDM cosmology.

Alain Blanchard
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Re: [astro-ph/0311381] The XMM--NEWTON Omega Project: II.Cos

Post by Alain Blanchard » February 07 2006

Niayesh Afshordi wrote:I stand by my previous statement.

The theoretical statement that we prove in Afshordi & Cen 2001 is that, in the absence of non-gravitational heating , T \propto (HM)^{2/3}, if mass is measured within a fixed overdensity with respect to the critical density of the universe.

However, if we fix overdensity with respect to the critical density, i.e. \Omega_M \Delta(z,\Omega_M) = const., Eq. (2) in Vauclair et al. implies that T \propto (1+z) M^{2/3}, which is inconsistent with above theoretical expectation for \Lambda CDM cosmology.
I insist!

Any definition is legitimate of course. But one should be self consistent:

The mass function we used is defined with contrast relative to the background!
So we used scaling law for contrast relative to the background.

Your scaling is correct as well, but you cannot use it in the mass function to derive N(T), unless you find the theoretical expression for the mass function for clusters defined
relatively to the critical density (which I am not aware to exist).

Of course the final N(T,Z) should be the same INDEPENDENTLY of the definition used.

In short : using overdensity with respect to the critical density in Vauclair et al would be inconsistent.

By the way, you can check that our colleagues (Borgani, Henri, Eke, Viana,etc...) used the same definition than us.

Cheers,

Alain Blanchard

Alain Blanchard
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Re: [astro-ph/0311381] The XMM--NEWTON Omega Project: II.Cos

Post by Alain Blanchard » February 07 2006

Niayesh Afshordi wrote:I stand by my previous statement.

The theoretical statement that we prove in Afshordi & Cen 2001 is that, in the absence of non-gravitational heating , T \propto (HM)^{2/3}, if mass is measured within a fixed overdensity with respect to the critical density of the universe.

However, if we fix overdensity with respect to the critical density, i.e. \Omega_M \Delta(z,\Omega_M) = const., Eq. (2) in Vauclair et al. implies that T \propto (1+z) M^{2/3}, which is inconsistent with above theoretical expectation for \Lambda CDM cosmology.
Just to be sure that we understand:

if one defines objects with different definition (/background /or relative to the critical density)
than the mass M is NOT THE SAME for the same object and scaling with redshift in M-T are different accordingly.

Niayesh Afshordi
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Post by Niayesh Afshordi » February 08 2006

Alain,

I don't have any problem with your choice of mass definition. My problem is with your M-T relation. I judt don't see how you can justify its (1+z) dependence.

What I can tell you is that Eq. (2) in your paper does not work for any choice of \Delta(z,\Omega_m(z)), which is defined to be the contrast with respect to mean density of the Universe in your paper (Am I right?). For example, I know if you pick \Delta = 178/\Omega_m(z), the scaling with redshift is incorrect.

Now, it may be that if you choose \Delta = 178 (is this what you use for Jenkins mass function?), Eq. (2) is somehow correct, but I don't see any theoretical justification for it. May be you can let me know.

Alain Blanchard
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[astro-ph/0311381] The XMM--NEWTON Omega Project: II.Cosmolo

Post by Alain Blanchard » February 08 2006

Hello,


Let me bo more detailled.

The M-T scaling comes from : [tex]T = M/R[/tex]

with [tex]M = \rho_{ins} *R ^3[/tex]
( [tex]\rho_{ins} [/tex] being in the actual density in the cluster)

That is : [tex]T = M^{2/3} \rho_{ins}^{1/3}[/tex]


Now if you define clusters in term of contrast compare to the critical density [tex]\rho_c(z) [/tex]
you can write [tex] \rho_{ins} = \Delta * \rho_c(z) = \Delta H^2[/tex]

giving the scaling:

[tex] T = M^{2/3} H^{2/3} \Delta^{1/3}[/tex]

Which is your way to write the scaling relation.

Now we write contrast compared to the background density :
[tex]\rho_{ins} = \Delta * \rho_{back}(z) = \Delta* \Omega_0*\rho_c (z = 0) * (1+z)^3[/tex]

giving the scaling:

[tex]T = M^{2/3} (\Omega_0*\Delta)^{1/3} (1+Z)[/tex]

So your scaling relation is the SAME THAN Eq (2) in Vauclair et al. with different reference
(background /critical universe). So they can be both used for counts provide one works self consistently.

Do you agree?

Cheers,

Alain

Niayesh Afshordi
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Post by Niayesh Afshordi » February 08 2006

I see. Thanks Alain.

Here is the problem. Since we assume a fixed T_X, the two derivations are identical ONLY if T=M/R does not change with radius. That would require an isothermal dark matter profile, M ~ R, or \rho ~ R^{-2}.

However, we know that both simulations (NFW) and observations indicate a steeper density profile around cluster virial radii. Therefore, the two definition are NOT identical, and hence my confusion.

In our work, we assumed an NFW mass profile for the cluster, and thus I do not expect a straightforward \Delta-M conversion, as you indicate. The interesting coincidence is that, even you include all the gory details of the NFW profile, as well as the scatter in the initial conditions, T ~ (HM)^{2/3} remains pretty accuarte, as long as the mass is defined within a constant overdensity with respect to the critical density of the universe.

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Post by Alain Blanchard » February 08 2006

I agree with you that in order to go from one definiton to an other one needs some asumption on the density profile. In practice, scaling/viril radius seems to work in both observations (see for instance Vihklilin and Arnaud recent works) and numerical simulations (Bryan and Norman and successors), we have also check to some extent that various definitions make little changes
( astro-ph/0601402) in observed quantities.

Cheers,

Alain

Niayesh Afshordi
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Post by Niayesh Afshordi » February 09 2006

Alain,

I still cannot find any numerical/analytic paper which could show your 1+z scaling for a LCDM cosmology. May be you should be more specific.

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Post by Alain Blanchard » February 09 2006

Hi Niayesh,

I found your question interesting... as I used to think that all people who have work on cluster counts use dthis scaling!

I have gone through a rapid scan of some of the past litterature.

I proudly notice that we may well be the firstone to have explcit the scaling of M-T for various cosmology in Oukbir & Blanchard (1992) A&A 262 L210. But this is just an indication that we persist in our own way...

Others which I have explictely checked are:

Borgani 1999 ApJ 517 40 (Eq 5)

Henry 2004 ApJ 609 603 (Eq 13)

Although the explicite derivation might not be given.
Of course the reason for using this definition of mass and the resulting scaling expression is
due to the fact that the mass function is defined for objects with contrat defined relative to the background.

Cheers,

Alain

Niayesh Afshordi
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Post by Niayesh Afshordi » February 10 2006

Hi Alain,

Thanks for the references. However, none of them actually derive your M-T relation, but rather use it to analyze observations.

Now, we both agree that, as you elequently described above, for an isothermal profile, i.e. if T=M/R=const. or \rho \sim R^{-2}, the two M-T relations are consistent for different mass definitions. However, we know that the mass profile is not isothermal in the outskirts. For NFW profile, \rho \sim R^{-3} in the outskirts, or in other words, mass grows logarithmically with R. Now, let us compare the two M-T relations when cosmological constant dominates:

1- In the accelerating regime, H, as well as critical density, go to a constants. Also, we expect the accretion into the DM halo to go to zero, and thus the mass profile (scale radius and central density) should remain, more or less unchanged. Therefore, the mass within surfaces of constant overdensity relative to the critical density reach an asymptotic mass, which does not change with time. You also expect, the temperature to remain constant, as little further meregr/activity is happening in the accelerating regime. This is all consistent with

T \sim (HM)^{2/3} \Delta^{1/3}

scaling relation.

2- On the other hand, if you look at surfaces of constant overdenity relative to the mean density of the universe, [tex]\bar{\rho}[/tex] ~ a^{-3}, given the NFW profile, we see that R \sim a. However, the mass enclosed only grows logarithmically with a. Then, the scaling relation

T \sim M^{2/3} (\Omega_0*\Delta)^{1/3} (1+z)

implies that the T drops as [tex]a^{-1}(\ln~a)^{2/3}[/tex]. However, this is inconsistent with the intuition that ceasure of merger activity in the acceleration dominated regime would lead to constant temperature.

This is why I think (1+z) scaling sounds unphysical in a \Lambda CDM cosmology.

Alain Blanchard
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[astro-ph/0311381] The XMM--NEWTON Omega Project: II.Cosmolo

Post by Alain Blanchard » February 10 2006

What you say I think is that the reference Radius to be used for scaling relation of temperature
should rather be set at a fixed contrast density compare to the critical density (even if the mass function appears self similar at the conventional virial radius). I am very open to this possibility which sounds physically motivated as you emphasize. I think astro-ph/0412161 is related to this type of consideration.

I did made a quick evaluation of the whether the evolution in the scaling relation would be affected
by this and I found that it makes a 10% change for an NFW profile (at z = 1), in the sense that clusters
in the past would be slightly hotter if exact scaling would work at fixed contrast density compare to the critical density.


Now to come back to the initial question, the basic validity of the Vauclair et al. results, I am considering that this type of possibility is within the typical type of uncertainty we have considered. In addition it will go in the sense of the discrepancy of [tex]\Lambda[/tex]CDM with observed clusters number counts being even worse. So our claim remains very robust.

Cheers,

Alain

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