Sunyaev-Zel’dovich Effect in WMAP Data Jose M. Diego & Bruce Partridge

Concordance Model . The X-ray We present a practical and powerful example of stacking astrophysical data profile (left) and WMAP SZE are applied to the detection of the Sunyaev-Zel’dovich effect (or SZE) in galaxy shown on the left panel (solid lines) compared with a polytropic model clusters and using WMAP 5 year data. Earlier works have reported a lack of that seems to accomodate all the available observations (dashed line). SZE signal in WMAP data (e.g Lieu et al. 2006). Several reasons have been A point source with a flux in the propossed to explain the apparent defficit. For example, contamination from range 10-30 mJy has been subtracted from this model to point sources, presence of relativistic electrons, different gas profiles. In this account for radiosources and work we use a large sample of galaxy clusters and look for the average SZE sources inside the galaxy clusters (dotted line). Actual signal in these clusters by stacking the CMB WMAP data in an area around observations of radiosources in the Q band (Lin et al. 2009) observe an them. The stacking procedure reveals a strong SZE signal at the position of the average flux of about 12 mJy in clusters. Our results show that assuming a more realistic profile for the gas in galaxy clusters, in agreement with the point source contamination the cluster can explain the apparent defficit of SZE and make it consistent with predicted by our concordance model. The same model predicts the correct predictions based on X-ray observations. We also investigate the possible amoount of observed X-rays except contamination from radiogalaxies and infrared sources and find that a model in the very center where more other phenomena (not considered in our accounting for realistic levels of the contamination is able to agree better with model) occur. the average X-ray and signal from galaxy clusters. By adjusting the parameters in the polytropic model we are able to find a model that Using a catalog with 750 X-ray selected clusters fits the observed average cluster profile both in the X-ray and microwave bands (see we obtain the average cluster signal from these figure above). The model has parameters which are consisten with current clusters in the ROSAT all sky maps (see left observations of galaxy clusters made by Chandra and XMM. This model leaves also figure). The average signal is obtained after room for non-thermal effects included in our analysis which might affect specially stacking 750 fields of 2.5 degrees around each the X-ray brightness. Some of these effects include shock waves and clumpiness cluster. The stacking procedure results in an that might boost the X-ray flux withouth affecting much the SZE signal. Because of average cluster with good statistical properties. these and other mechanisms, a succesfull model has to predict slihghtly less X-ray The average cluster has spherical symmetry, it is emission in the wings of the one dimensional profile. Our model overpredicts the x- not dominated by outliers and it obeys scaling ray emission at the center of the cluster but this is normal given the fact that we laws like the L-T and R-T relations. The stacking have not included phenomena such as cooling flows that mostly change the process has also another very important brightness at the center of the clusters. The model presented in the figure above also advantage; it reduces the fluctuations of the leaves room for possible contamination from point sources inside the galaxy Average X-ray cluster obtained after stacking the ROSAT surrounding background to a nearly constant fields around 750 known X-ray clusters. Also shown are the clusters. Current observations made by Lin et al. (2009) in the Q band revela that on field. In the case of the stacking of the CMB intrinsic PSF of ROSAT (left), the PSF of the stacking of average we should expect of the order of 10-15 mJy contribution from radio sources HEALPIX maps (middle) and the PSF of the stacking of the fields this will become a mayor advantage since original ROSAT maps (right) of 12 arcminute pixels. in a sample of clusters similar to the ones considered in this work. When removing a it removes the dominant CMB fluctuations. mean signal of 16 mJy in the Q band and in the model presented in the above figure, the predicted signal reproduces well the observed mean signal in clusters indicating that the model, although not being perfect is close to reproducing the observed average signal from clusters. B1 B2 P1 From this work we can derive several important conclusions. 1) The earlier B4 P2 B3 reported disagreement between the expected SZE signal and the observed one is most likely due to the fact that earlier works used a Beta-model to predict the SZE from X-rays. In this work we show that the Beta-model overpredicts the SZE by about a factor two when the model is fitted to X-rays. B4 Dependence of the Beta-model with the exponent beta and Changing the exponent beta in the comparisson with the observed X-ray and SZE profiles. The dotted line corresponds to beta=0.5, dashed line to the standard B1 profile does not help to reduce this beta=0.66 and dashed line to beta=0.8. Higher beta values can problem. In the figure to the right we fit better the SZE profile but fails at describing the X-ray B3 P1 emission in the wings of the one dimensional profile (left). P2 show three examples where beta is B2 changed from 0.5 to 0.8. Higher values of the exponent beta help reduce the SZE but at the expense of under- predicting the X-rays. Realistic values of beta overpredict the SZE flux by a

Stacked WMAP data (left) and one dimensional profiles (right) for WMAP and X-ray data. The data on the right panels is factor about two. 2) A polytropic compared with a variety of models. The X-ray plot(top) shows the difference between the observed and predicted X-ray profile. model with a profile steeper than the Beta-model is able to match both X- The stacking of WMAP data around the position of the known 750 X-ray clusters ray and SZE observations and predict reveals a strong SZE signal specially in the W band (left figure, top) and correctly the amount of point source also in the (left figure, middle). The Q band (left figure, bottom) still shows a contamination in the Q band. At higher signal at the position of the clusters but weaker than in te other two cases, due mostly the polytropic model to the poorer resolution of thye Q band that dilutes the signal but also to a more likely predicts a contamination level of about point source contamination. The above esult was obtained after masking the brightest 20 mJy while based on current Using the best polyropic model the predicted SZE flux is compared sources in WMAP data. If these sources are not removed, the negative decrement with the observed X-ray flux. This predicted correlation should be predictions we would expect about 10 confirmed by experiments like Planck, ACT, SPT or APEX. observed in the Q band disappears indicating that at thess frequencies, the point mJy thus suggesting that the model sources are a serious contaminat to the SZE. Not removing these bright sources in the still needs to be improved. 3) Using the polytropic model we can predict the SZE flux other two frequency bands, did not have a large impact although the SZE signal was for each cluster and compare it with the observed X-ray flux. The model predicts a reduced by a small amount in the V band and by a negligible amount in the . strong correlation between both the X-ray and SZE flux with a correlation exponent Fitting the X-ray and SZE data with analitical models revealed that the isothermal close to 1. Future experiments will be able to confirm this prediction. Beta-model was unable to reproduce well both data sets simulteneously in agreement with earlier works based on N-body simulations that suggested that a Beta-model can A C K N O W L E D G M E N T S not fit X-ray and SZE signals simultaneously. Other more accurate models should be This work was supported by a Ministerio de Ciencia e innovación grant JC2008-00104 and by the NSF grant used instead. In the right figures we show 6 models. Four of them are based on AST-0606975.

isothermal Beta-models (B) and two on the polytropic model (P) of Ascasibar & R E F E R E N C E S Diego (2008). The models are compared with the X-ray average profile (difference X- Y. Ascasibar & J.M. Diego. 2008, MNRAS, 383, 369. ray minus model) in the top figure and with the SZE profiles in the bottom figure. We J.M. Diego & B. Partridge. 2009, MNRAS submitted. arXiv.0907.0233 R. Lieu, J.P.D. Mittaz, S.N Zhang. 2006, ApJ, 648, 176 found that a Beta-model that fits the X-ray profile overpredicts the SZE signal by a Y-T Lin, B. Partridge et al. 2009, ApJ, 694, 1009 factor two while the polytropic models render a better fit.