Note: The next group meeting will be in the Courtyard on Monday Oct 2, 14:00 (unless a conflict emerges). What lensing observations might distinguish between different dark matter candidates or properties? Is there a need for currently-lacking simulations tailored to the masses or scales that lensing specifically probes? Etc. We may also see how much overlap there is in the end with the Baryons group and possibly merge the efforts.

Notes from Monday 25 Sep
(Notes in progress, please feel free to add material). The discussion concentrated on what the properties of dark matter might be, and how it might affect the inner core density in galaxies and substructure in galaxy or cluster halos. Limits from the Tremaine & Gunn argument [ref], Gilmore [ref], etc.

Tasks from Monday 25 Sep
  • Reference paper compilation on CDM measurements/estimates from lensing
  • What limits are there for the inner core density (from local dwarfs)
  • Dark matter candidates and their properties: cold/warm/hot, condensation scales, survivability in halos
    • Are there numerical predictions on relevant physical scales? Analytic predictions?
  • Detection techniques & methodologies, as a function of physical or mass scale

First Group Meeting: 10am Sept. 25, 2006

Suggestion for issues to address in a proceeding-type document could be:

1) What is the current LCDM paradigm (what are the basics theories and their parameters)?
2) What evidence is this based on?
3) What are the successes and (possible) failures of the current paradigm?
4) What modification of the LCDM paradigm have been suggested to resolve
some of the outstanding issues (eg cusps/substructure).

(In progress; Leon)

More specific questions [Tommaso]:

  1. Is there dark matter?
  2. Is dark matter cold/warm?
  3. Is dark matter interacting?

The cold dark matter paradigm makes specific predictionsbased on these assumption, e.g. dark halos should be cuspy, there should be substructure. Can lensing measure these quantities and help address the questions above?

[The following segue added by Phil 12/1/06 to bring coherence to this page]

It seems that one robust prediction of simulations that is testable using current lensing data is the NFW profile concentration at the cluster mass scale. The simulations predict c~7 or so, but some well-known strongly-lensing clusters have been found to show a higher concentration than that. Do we understand these results?

Is there a concentration problem?

The Cluster Concentration Study Group

Natarajan, Kneib, Dalal, Comerford, Gavazzi, Czoske, Soucail, Marshall, Ardis

Concentrations for clusters from other mass estimators (other than lensing)
[Posted by Priya]

1. Check out Table 2 and Figure 15 in paper by Rines et al. where they
are looking at the CIRS sample (2006 AJ 132 1275).
They found fairly good agreement with the predictions of the simulations
(notably Bullock et al. 2001 and Navarro et al. 1997), unlike the recent
lensing results. They find a few clusters that scatter to high
values like A1689, but I'm not sure how much of the scatter is physical
and how much is measurement uncertainty. The mean c values agree well,
though they don't see the weak dependence on mass (although I don't
think they can rule it out).

2. Earlier results from the CAIRNS sample Rines et al. again (cited in
the paper above) found higher values for concentration parameters.

3. There's a recent pair of papers on astro-ph (0610134, 0610135) that
use Chandra data for systems from galaxies to clusters to study the c-M
relation. They find essentially perfect agreement with the simulations,
which is interesting if true. These are both James Bullock showed at
the conference.

4. In recent work Limousin et al. (this is lensing) have done a very
careful mass reconstruction of Abell 1689 (Jean-Paul showed some nice plots from
this work in his talk if you all remember) and in fact they find
reasonable values of c.

Note that we need to be careful to see if the values quoted at c_200 or
c_101 or whatever.

Project suggestion:

May be we could think of making a cluster toy model(s) that we would then
run through by some interested people so that one could check the
output compared to the input, in the spirit of the STEP exercise.
We could start by doing first simple simulation and then
make them more and more complex to include the more realistic noise ingredients
(cluster contamination, realistic redshift distribution, galaxy mass component,
making real fits image including psf ...).

This is a great idea, will discuss putting this together this week at KITP [Priya]

The effect of substructure on the lensing-inferred concentration

This interesting preprint by Lindsay King and Virginia Corless looks at the effect of large substructures on
concentrations. They find that substructures that are 10-20% of the total mass of the cluster can, when aligned along the optical axis, increase the inferred concentration from 5 to up to 10 or so. If the same substructure is placed in the plane of the sky, the inferred concentration goes down (but only by a unit or so). Here are the two important figures:

KingCorless2006-figure2.jpg KingCorless2006-figure3a.jpg

The "high" concentration of MS2137-23; a test case

This paragraph summarizes this paper (gavazzi 05) which builds on (gavazzi et al. 03).
I modeled the strong+weak lensing data in this *well relaxed* cluster at z=0.31 (strong lensing: 2 sources at z=1.501 one producing a radial arc and the second one producing the tangential arc). For weak lensing I took advantage of good photometric redshifts (UBVRI from FORS2@VLT and JK from ISAAC@VLT on a somewhat smaller fov), thus allowing a clean removal of cluster members. So I expect the dilution to be kept at a low level. Although weak lensing data extend down to ~900 kpc, the availability of radial+tangential arcs already puts tight constraints on the density profile and strong lensing alone points toward a rather high concentration (c200~12).

There are several pieces of evidence that the halo may be elongated along the line of sight (discrepancy X-rays and lensing mass profiles + the misalignement between DM halo and the central BCG major axis). Since the response of lensing and X-rays signal to such an elongation differ, it may explain the discrepancy. I also discuss this asphericity effect in a more general context.
As I said this morning during our discussion, for an elongated halos (with axis ratio q along the los), the mass estimate is boosted by this factor q whereas the rs parameter is left unchanged. Therefore, assuming M200~r200^3, one finds that c_prolate = q^1/3 c_spherical (q>1 if prolate and elongated along los and q<1 if oblate and flattened along los). Hence an elongated halo will tend to look more concentrated!! In addition, most cluster detection methods are more or less biased toward elongated halos. The mean amplitude of this bias would likely depend on the detection method (richness, X-rays, lensing) and it remains to be evaluated and added to the trend already pointed out by Neal in his simulations.

In addition one should keep in mind that *Well relaxed* means old and old means more concentrated for a given mass (cf eg J. Bullock's talk during KITP conference). Also, strong lensing occurs at small scales in this cluster (especially the radial arc) and this mean that the cD galaxy may change the total density profile (although it is taken into account in the modeling).

In conclusion I would say that the 'high' concentration of MS2137 is observationally robust. However it does not seem to me that there is any tension with CDM predictions.

[If one is interested in redoing the weak lensing + zphot analysis "from scratch", I can provide the VLT images. Together with the WFPC2 image for strong lensing, the validity of our treatment can be entirely cross-checked].

Effect of triaxiality
[Masamune Oguri]

In my paper (Oguri et al. 2005) I studied the effect of triaxiality on the determination of the concentration parameter c_vir. In particular I did a simple test by putting an analytic triaxial halo (with c_vir=4, a/c=0.4, and b/c=0.7) and projecting it along three principal axies. For each projected kappa map I compute 2d radial profile of kappa, add A1689-like noise, make ''observed'' radial profile of kappa and use it to constrain c_vir assuming spherical symmetry (what people usually do).
The Figure summarizes the result. The filled square indicates the true value you get when the triaxial halo is spherically averaged. The contours are inferred values from 2d kappa profile. Upper right one corresponds to the case we see the halo from major axis, whereas lower left one is from minor axis. It is clear that the triaxiality induces the systematics depending on the projection direction. When we see the halo from the major axis, we significantly overestimate both c_vir and mass (more than 3sigma level in this test case) if we simply assume the spherical symmetry for this halo; the inferred c_vir is larger than true value by ~30%. On the other hand we underestimate c_vir by ~30% if projected along minor axis. This, in turn, indicates that the constraint on c_vir becomes less restrictive if we adopt a traiaxial halo in fitting the 2d kappa map (see the top panel of Figure 3 in the paper). Note that lensing bias prefers the major axis aligned with los direction. The difference between X-ray and lensing mass for high c_vir clusters also implies the major axis-los alignment (see also Raphael's paper above). The effect of triaxiality is somewhat compensated by c_vir-triaxiality anti-correlation (see Jing & Suto 2002), but it's still notable.

More notes on concentrations in the (X-ray?) literature
[Eran Ofek]

I compiled the attached list in the year 2000 (based on: Wu &Xue 2000; Wu 2001).
Wu & Xue (2000) claimed that there is a simple relation between
alpha, T, and R_s (which are listed in the attached Table)
to rho_s, so it is possible to calculate c_vir (Just below Eq.4 in their paper).

I used this list to calculate c_vir as function of M_vir and compared
the results with the Bullock et al simulations.

Also attached is a plot I made 6 years ago:
$c_{vir}$ vs. $M_{vir}$ for the $57$ clusters.
Triangles - cooling flow systems ( I guess its meaningless)
Circles - non cooling flow systems
Open markers - clusters with z>0.1
Filled markers - z<0.1
Solid lines are the Bullock et al. (2000)
predictions for z=0 (blue) and z=0.3 (red).
dashed lines shows the predicted 1sigma scatter in c_vir.

I have similar plots for non-standard cosmologies.

If you are interested, I can search for the programs I used
to calculate c_vir...

How much volume do we need to survey before a cluster like MS2137 (i.e. c = 12) is detected?
[Neal, posted by Priya]

Eyeballing from the figure (Neal's figure that he mentioned in the discussion), it looks like you'd find a
cluster with apparent c_2D = 12 in about 1 (Gpc/h)^3 volume. So it doesn't seem crazy. You wouldn't expect
a c_2D this high for a typical lens, but it's not absurd to find such objects given modern survey volumes.

The effect of cooling on concentration

At the last meeting, I said I'd look into how much gas cooling could increase halo concentrations for our
lensing clusters. A rough estimate of this can be obtained using simple adiabatic contraction models. I took
Oleg's 'contra' code and computed the shear profile corresponding to different cooled masses. Then I fit the
resulting lensing observables to a spherical NFW model : the fitted quantities were the strong lensing critical
radius and the gamma_tan profile. The result is below:

This example was for a M=10^15 NFW halo with c_vir=5 originally. For cooled masses of 1-3 * 10^13,
one can increase the inferred c_vir by 50%.

In his talk, Andrey showed a figure indicating that gas cooling & star formation could raise the concentration
up to c~10 or so, even for halos at 10^14 Msun/h. I'm not sure how overcooled that simulation was, so it's
unclear whether the simple estimate above would be consistent with their simulation.

Possible explanations for the Ultra-High concentration in Cl0024+52

In Kneib et al (2003) we analysed a large, sparse mosaic of WFPC2 images,
extending to a radius of 11 arcmin or so, covering the field of the merging
cluster Cl0024+52. In the weak lensing mass map you can clearly see a secondary
mass clump to the North West of the main cluster component. The ellipticity
catalogue was masked within the central 100 arcsec as the contamination by
bright cluster members is very high here - not so much their own ellipticity but
rather the lensing and masking effects the bright members have on the backgound
galaxies. The HST mosai was single filter: the weak lensing sources were
selected using their faint magnitudes alone. The HDF redshift distribution was
used to estimate the median redshift of background galaxies in images of the
given depth - this was determined to be z=1.1.

We fitted two mass components to the ellipticity data, allowing positions,
masses and concentrations to vary. To the central clump we applied a strong
lensing prior, anchoring the position of the clump to that found in the strong
lensing analysis and constraining the Einstein radius to be that of the strong
lens model (within a Gaussian prior defined by the error bar). There is not much
more strong lensing information than this - there seems to be just one dominant
multiple image system forming a broken Einstein ring.

The concentration of the central clump was found to be 22{+9/-5}. The second
clump (comprising some 30% of the total cluster mass) was found to have a lower
concentration (~4).

With the paucity of weak lensing data in the central region, and the lack of any
further strong lensing information, the central component of Cl0024+52 is
somewhat under-constrained, and I guess susceptible to systematic errors. To
address some of these I re-did the analysis using critical densities for the
weak lensing catalogue that were 8% lower and 14% higher than the fiducial value
- these correspond to source plane redshifts of 1.3 and 0.9 respectively. Using
a different critical density is equivalent to applying a shear calibration
factor to the data, of the kind often needed in weak lensing analyses (see the
STEP papers for examples - 5-10% is not unheard of).

The higher critical density (z=0.9, or 14% understimated shear) gave a lower
concentration value: 14[+5/-3]. Similarly, the lower critical density gave a
higher concentration.

In general one would expect shear to be underestimated: PSF roundening, and
catalogue dilution by foreground and cluster members both do it. More subtly,
catalogue dilution would mean that we overestimated the number density of background
galaxies, and a lower background number density is indicative of a shallower depth and
lower median redshift. To get an overestimated shear value you need, for
example, coherent tangential residual PSF contamination. This is usually picked
up on... It has been suggested that using the HDF redshift histogram introduces
some uncertainty just due to the cosmic variance associated with such a small field.
I don't know which way it goes though.

I also re-did the analysis using just a single mass component, as would be done
by the simulators when deriving their predicted concentrations from their synthetic clusters.
Since the substructure is offset from the optic axis we see the second effect predicted by
King and Corless, i.e. that the inferred (single clump) concentration is lower than the double
clump analysis value. With the fiducial critical density I get c=16[+5/-3]; with the higher critical
density (z=0.9, or 14% understimated shear) I get c=12[+3/-2].

On top of all this we have the observation of Czoske et al (2002) that there is
significant line of sight mass structure, which would lead to a higher projected
concentration than would be measured by a simulator.

I conclude that we may well be seeing a collection of effects in this cluster
all of which combine to increase the inferred concentration. The concentration
corresonding to that predicted from simulations may well be less than 12 and so
pose no "problem."

Draft Proceeding LCDMKing