We plan to start a discussion session on the SZ power spectrum, which is a good example of the crossroad of cosmology and astrophysics. Below, we listed references on recent observational and theoretical results as well as topics proposed for discussions. Daisuke

How robust is the current theoretical template? What's the extent of astrophysical uncertainties?

Non-thermal pressure: dependence on radius, mass, redshift, dynamical states

Stellar+AGN feedback: efficiency

Stellar fractions in Groups and Clusters: normalization, mass and z-dependence

What kind of observations can help constrain/improve the tSZ template?

X-ray observations of groups: scaling relations, sample selection function, z-evolution, prospects of improving them, how about stacking?

SZ observations: pressure profiles in the outskirts of clusters. how about groups? How clumpy is the ICM?

Accurate measurements of stellar mass fraction: contribution of ICL in groups, redshift dependence

Contribution from point sources (infrared SF galaxies and AGN) may still be a concern, but there are interesting astrophysical aspects from their roles.

What's next?

kSZ power spectrum at the verge of detection (?). Note that the kSZ power is primarily due to (a) Ostriker-Vishniac (OV) effect and (b) patchy reionization. Need an accurate model of the OV effect to go after the patchy reionization signal. kSZ signals from patchy reionization, in turn, provides unique constraints on the duration of reionization (complementary to Planck and WMAP polarization measurements). The kSZ power is also important for the interpretation of the tSZ power measurements as well.

Theoretical challenge: Is the OV template accurate enough to constrain patchy reionization? Major uncertainty: baryonic physics in linear to mildly non-linear regime? What do we know about feedback effects in IGM?

Observational challenge: modeling out sub-mm galaxies, need Herschel (SPT+Herschel proposal)?

Discussion 1, February 16 (Notes from D. Nagai)

Current status:

Observations: tSZ power spectrum has been detected and shows lower than expected to power. Sigma8=0.771+-0.013 inferred from the SZ power spectrum is thus lower compared to other measurements: Sigma8=0.82+-0.02. (From Neelima: WMAP7+BAO+SN for a wCDM model gives Sigma8=0.802+-0.038, so the question of whether there is any tension is up for debate, see http://lambda.gsfc.nasa.gov/product/map/dr4/params/wcdm_sz_lens_wmap7_bao_snconst.cfm).

Theory: new models (including non-thermal pressure+feedback) seems to reconcile this discrepancy. The recent Battaglia, Shaw, Trac are roughly consistent, and all are systematically lower than the Sehgal template originally used in ACT and SPT analyses.

Where do most of the tSZ power come from?
Answer: Outskirts of low-mass, high-z groups for which we have little observations at present. (The numbers here are bogus, see the update/clarification on the first item in Discussion #2 below.)

1/2 comes from r>r500. => it was pointed out that this may be template dependent. this is important for determining the usefulness of the stacking analyses of X-ray groups (which would be limited to r<r500). (From Neelima: For the Arnaud et al. 2010 model, less than 20% is from r>r500, but this percentage can increase or decrease with different profiles.)

1/2 comes from z>1

1/2 comes from M>1e14 Msun (From Neelima: these two points are also model dependent. Figure 6 of Trac, Bode, Ostriker 2010 shows a nice illustration of the contributions of different mass and redshift ranges for different models.)

How secure is the current tSZ power spectrum measurements?

Removal of sub-mm galaxies: SPT cross-correlate 150 and 220GHz bands in the past. this will be done better with Herschel follow-up of 100 sq.deg. SPT field, including clustering of sub-mm galaxies. This will be done in the near future (likely this year).

homogeneous kSZ template is subtracted. This is basically linear-theory calculations and should be sufficiently accurate. Baryon suppression (due to gravitational heating or feedback in IGM) might affect the kSZ template a bit, but there are constraints from the Ly-alpha forest!

patchy kSZ depends on the duration of reionization, highly uncertain. but, the total kSZ power will be measured soon with SPT+Herschel, so can just subtract the total kSZ contribution, providing accurate measurements of the tSZ power soon.

How robust is the current tSZ template?
1. Nonthermal pressure and z-dependence

how good is invisid fluid approximations? how about physical viscosity?

how about MHD, conduction, non-equilibrium electrons?

CRs and B-field are additional sources of non-thermal pressure. CR's contribution is expected to increase with radius, but the amplitude is probably smaller than that of gas motions.

2. Energy feedback and stellar fractions are also uncertain

What more can be done observationally ? (from Ming)
1. Try X-ray observations with different selection functions of groups and clusters to better understand P(M_gas | M, r, z), at least locally. (a small but not trivial point about the Sehgal template: they used the Vikhlinin et al. 2006 and Sun et al. 2009 to calibrate the halo gas fraction. Vikhlinin et al. 2009 added more clusters and the average cluster gas fraction decreases by ~9%. The Chandra M-Y_X relation from Vikhlinin et al. 2009 and Sun et al. 2009 agrees very well with the XMM result on the REXCESS clusters. If Sehgal et al. had the Vikhlinin et al. 2009 data to calibrate, their power will decrease by 10-15%. This shows how sensitive the template is to the local constraints of the halo gas fraction.)
2. The dependence of mass bias with radius and mass needs to better constrained.
3. For low-mass systems at high-z, can we try stacking for the slope of surface brightness profile at beyond r_2500 - r_500 ? What about stacking SZ data for these low-mass systems?

New approaches/techniques:
1. Cross-correlating optical+SZE in a given z bins

can tell us where signals come from (should be tried e.g., with DES)

halo model approach could be useful here

2. Stacking

challenges: need to know virial radius and selection functions

3. IRAC-selected clusters may also be z-independent at z=1-2 (the shifting of the stellar emission peak) and many of them have low mass. However, it was mentioned that they are not always confirmed from X-ray follow-ups.
4. Is power spectrum optimal estimator? or is there even a better basis for tSZ?

Questions for future discussions:

Can we really do cosmology with the SZ power spectrum? e.g., Is the template robust enough to push precision measurements of sigma8?

What kind of cluster physics can we learn if we had very precise tSZ power spectrum measurements?

Discussion 2, March 8 (Notes from D. Nagai)

1. Clarification on where 1/2 of the power comes from. There have been some concerns if the answers are model-dependent. We have now checked this using three different models by Battaglia, Shaw, and Trac. Findings are reported below.

mass above M500 of 2e14 Msun almost exactly (Battaglia, Shaw, Trac)

radial range: 20-30% of the SZ power comes from outside of r500 @ l=3000, depending somewhat on the model; Based on the Battaglia's model, 20% for non-radiative sim, 25% cooling, 30% for cooling+AGN. Note that this is computed by smoothing near r500 to avoid supurious power due to sharp cuts.

2. Discussions on theoretical modeling of the SZ power

The SZ power comes from "far-field", tough for semi-analytic approach since "ratty" areas (D.Bond)

But, the pressure profile agree up to r=10 x r500, albeit contribution from SZ substructures and filaments. (M.Arnaud)

Non-equilibrium effects are very important for modeling the SZ power: (1) residual gas motions due to incomplete thermalization, (2) CR pressure support, and (3) non-equilibrium electrons.

Non-thermal pressure fraction is "astoundingly" large at the large-cluster centric radii. Q. Do simulations adequately capture the nature of gas motions? A. It is really the problem of how clumps slow down, rather than dissipation of turbulent flows, so the hydro sims should do fine. (Pkin/Ptot)~1 at r=3xr500. We should visually show what we see this in sims.

We need a more continuous quantity to characterize the "relaxed" and "unrelaxed" clusters. Could Pkin/Ptot be one? But, we need some connections to observables! Could use more ideas here.

To improve the accuracy of the model, we must take into account (1) rise of kinetic pressure support with radius, (2) AGN feedback, but also (3) baryonic effects on the DM distribution, which is not accounted for in the painting on the DM sim approach.

homogeneous kSZ should be robustly predicted, but need big box to compute where the velocity power spectrum is peaking

patchy reionization is still uncertain; not surprised different by a factor of 10, but ionizing bubbles with v~100-200 km/s

3. Observational Approaches and Challenges

Can we detect gas motions in cluster outskirts with oxygen absorption lines. Do we expect shifts or broadening? (M.Donahue)

Stacking approach seems attractive at first, but there are problems and challenges. First, we need something to stack on. But, optical selection is a problem -- adds to the denominator, but not numerator. Sloan cluster also have large dispersions, so worry about the non-Gaussian scatter. How about X-ray selection? e.g., MaxBCGs catalog was used to go down in mass. But, for many groups, we will just see cool core regions, so we will be stacking cool core regions.. Clumping is also an issue for stacking the outskirts of X-ray groups and clusters. How about stacking SZ? SZ confusion kick in at M~1e14Msun.

CLASH sample with X-ray+Lensing datasets may be useful for calibrating massive clusters at z=0.3-0.8.

IR point sources removal will be done better with Herschel soon. We will need to first nail down the clustering component of the IR sources.

4. What can the SZ power spectrum teach us?

Many thought that cosmology with the SZ power spectrum is hard. But, the SZ power depends extremely sensitively on sigma8, Cl~sigma8^7-9. So, the sigma8 measurements should tighten up considerably once we combine the full ACT, Planck, SPT datasets. Could this be the most robust measurements of sigma8? It is unclear at the present (many are skeptical). The SZ power may not be suitable for the most robust w measurements.

But, the shape of the SZ power spectrum might shed some lights on cluster astrophysics! We aren't getting the shape information yet -- mostly talking about the power at l~3000. But, the shape measurements will likely improve greatly over the next few years. The shape depends sensitively on the input cluster physics. So, we can hope that ACT and SPT can shed some light on this. To list some ideas discussed at the today's meeting, the SZ power spectrum can probably tell us something about (1) feedback operating on high-z groups, (2) how energy injection rate as a function of z, (3) the relative importance of non-thermal pressure and AGN feedback, and (4) if there are a lot of outflowing phenomena especially above z>1.

D.Bond pointed out that there will be a major move forward from ACT/SPT to ACTpol/SPTpol. In addition to the polarization data, the enhanced detector sensitivities should also improve the total anisotropy measurements considerably, which should also help with cluster finding. So, we can expect cleaner separation of different components. But, D.Marrone pointed out that both ACT and SPT are giving up colors (e.g., 220GHz, but no 275GHz for ACT).

5. Questions for the next discussions

For cosmological parameter estimation, we will need an efficient method. A simple analytical prescription is required to search parameters space spanned by both cosmological and astrophysical parameters. If so, what would be the optimal strategies for taking advantage of the information provided by the high-res. sims of individual clusters and large lower-res. sims, and incorporate the physical insights from these sims into the analytical model?

Do we really have a tension between the cluster abundance and SZ power spectrum measurements?

A_sz vs. sigma_8? A_sz less dependent on model and l..

Remaining differences among models, especially at low-l and high-l, good agreement around l~3000 (fortuitous?)

ReferencesTopics for discussionTheoretical challenge:Is the OV template accurate enough to constrain patchy reionization? Major uncertainty: baryonic physics in linear to mildly non-linear regime? What do we know about feedback effects in IGM?Observational challenge:modeling out sub-mm galaxies, need Herschel (SPT+Herschel proposal)?Discussion 1, February 16 (Notes from D. Nagai)Current status:

Observations:tSZ power spectrum has been detected and shows lower than expected to power. Sigma8=0.771+-0.013 inferred from the SZ power spectrum is thus lower compared to other measurements: Sigma8=0.82+-0.02.(From Neelima: WMAP7+BAO+SN for a wCDM model gives Sigma8=0.802+-0.038, so the question of whether there is any tension is up for debate, see http://lambda.gsfc.nasa.gov/product/map/dr4/params/wcdm_sz_lens_wmap7_bao_snconst.cfm).Theory:new models (including non-thermal pressure+feedback) seems to reconcile this discrepancy. The recent Battaglia, Shaw, Trac are roughly consistent, and all are systematically lower than the Sehgal template originally used in ACT and SPT analyses.Where do most of the tSZ power come from?

Answer: Outskirts of low-mass, high-z groups for which we have little observations at present. (The numbers here are bogus, see the update/clarification on the first item in Discussion #2 below.)

(From Neelima: For the Arnaud et al. 2010 model, less than 20% is from r>r500, but this percentage can increase or decrease with different profiles.)From Neelima: these two points are also model dependent. Figure 6 of Trac, Bode, Ostriker 2010 shows a nice illustration of the contributions of different mass and redshift ranges for different models.)How secure is the current tSZ power spectrum measurements?

How robust is the current tSZ template?

1. Nonthermal pressure and z-dependence

- how good is invisid fluid approximations? how about physical viscosity?
- how about MHD, conduction, non-equilibrium electrons?
- CRs and B-field are additional sources of non-thermal pressure. CR's contribution is expected to increase with radius, but the amplitude is probably smaller than that of gas motions.

2. Energy feedback and stellar fractions are also uncertainWhat more can be done observationally ? (

from Ming)1. Try X-ray observations with different selection functions of groups and clusters to better understand P(M_gas | M, r, z), at least locally. (a small but not trivial point about the Sehgal template: they used the Vikhlinin et al. 2006 and Sun et al. 2009 to calibrate the halo gas fraction. Vikhlinin et al. 2009 added more clusters and the average cluster gas fraction decreases by ~9%. The Chandra M-Y_X relation from Vikhlinin et al. 2009 and Sun et al. 2009 agrees very well with the XMM result on the REXCESS clusters. If Sehgal et al. had the Vikhlinin et al. 2009 data to calibrate, their power will decrease by 10-15%. This shows how sensitive the template is to the local constraints of the halo gas fraction.)

2. The dependence of mass bias with radius and mass needs to better constrained.

3. For low-mass systems at high-z, can we try stacking for the slope of surface brightness profile at beyond r_2500 - r_500 ? What about stacking SZ data for these low-mass systems?

New approaches/techniques:

1. Cross-correlating optical+SZE in a given z bins

- can tell us where signals come from (should be tried e.g., with DES)
- halo model approach could be useful here

2. Stacking- challenges: need to know virial radius and selection functions

3. IRAC-selected clusters may also be z-independent at z=1-2 (the shifting of the stellar emission peak) and many of them have low mass. However, it was mentioned that they are not always confirmed from X-ray follow-ups.4. Is power spectrum optimal estimator? or is there even a better basis for tSZ?

Questions for future discussions:

Discussion 2, March 8 (Notes from D. Nagai)1. Clarification on where 1/2 of the power comes from. There have been some concerns if the answers are model-dependent. We have now checked this using three different models by Battaglia, Shaw, and Trac. Findings are reported below.

2. Discussions on theoretical modeling of the SZ power

3. Observational Approaches and Challenges

4. What can the SZ power spectrum teach us?

5. Questions for the next discussions