1. Moscow (20/12 - 24/12, 2004) 1 Cosmology and High Energy Astrophysics (Zeldovich 90) Comparing the temperatures of Galaxy Clusters from hydro-N- body simulations to Chandra and XMM observations P. Mazzotta University of Roma “Tor Vergata” And Harvard-Smithsonian Center for Astrophysics E. Rasia, S. Borgani, S., K. Dolag, L. Moscardini, G. Tormen

2. Moscow (20/12 - 24/12, 2004) 2 Cosmology and High Energy Astrophysics (Zeldovich 90) Common misconceptions about temperatures Outline of the talk I will introduce a new temperature estimator that better approximate the projected X-ray temperature Common misconceptions: projected X-ray temperature = T ew Discuss some (cosmological) implications for the determination of  8 via the XTF

3. Moscow (20/12 - 24/12, 2004) 3 Cosmology and High Energy Astrophysics (Zeldovich 90) Projected Gas Temperature Gas temperature distribution One (or more) Observer(s) Projected gas temperature

4. Moscow (20/12 - 24/12, 2004) 4 Cosmology and High Energy Astrophysics (Zeldovich 90) Temperature maps of simulated Clusters Nagai & Kravtsov, 2002, ApJL  T

5. Moscow (20/12 - 24/12, 2004) 5 Cosmology and High Energy Astrophysics (Zeldovich 90) Temperature maps of Clusters Observed with Chandra MKW 3S A36672A 0335 Mazzotta et al. 2002, ApJL, 567, 37 Mazzotta et al. 2002, ApJL, 269, 31 Mazzotta et al. 2003, ApJ, 596, 190

6. Moscow (20/12 - 24/12, 2004) 6 Cosmology and High Energy Astrophysics (Zeldovich 90) How do we compare temperature maps obtained from Hydro+N-body simulation with the ones obtained from the data analysis of X-ray observations?

7. Moscow (20/12 - 24/12, 2004) 7 Cosmology and High Energy Astrophysics (Zeldovich 90) Temperature from hydro-N-body simulations: mass and emission-weighted temperature projected temperatures are obtained by simply calculating the mean weighted value of the gas temperature along the line of sight: Mass weighted Emission-weighted Physical meaning: it gives the gas total thermal energy Introduced because it should provide a better estimate of the observed temperature Weights more the densest cluster regions

8. Moscow (20/12 - 24/12, 2004) 8 Cosmology and High Energy Astrophysics (Zeldovich 90) Spectroscopic projected temperature From an X-ray observation point of view the cluster gas temperature is derived through the fit of a thermal model to the observed spectrum. From an X-ray observation point of view the cluster gas temperature is derived through the fit of a thermal model to the observed spectrum. Measuring a projected temperature is thus equivalent to find a thermal model with a temperature T spec whose spectral properties are as close as possible to the properties of the projected spectra. Measuring a projected temperature is thus equivalent to find a thermal model with a temperature T spec whose spectral properties are as close as possible to the properties of the projected spectra.

9. Moscow (20/12 - 24/12, 2004) 9 Cosmology and High Energy Astrophysics (Zeldovich 90) Spectroscopic projected temperature The emission spectrum can be written as: The combination of two thermal bremsstrahlung is not a thermal bremsstrahlung T spec is not a well defined quantity A proper comparisons between simulations and observations requires the simulation of the spectra of the clusters via a X-ray observatory simulator like X-MAS +line emission

10. Moscow (20/12 - 24/12, 2004) 10 Cosmology and High Energy Astrophysics (Zeldovich 90) T spec Fitting two-temperature thermal spectra with single-temperature models: Z=0 T=10 keV T=1 keV T=2.5 keV T=5 keV T spec

11. Moscow (20/12 - 24/12, 2004) 11 Cosmology and High Energy Astrophysics (Zeldovich 90) T ew v.s. T spec : Z=0 T ew Overpredicts T spec Discrepancies as large as 60% If T 1 >2 keV the two temperature source spectra can be fitted by a single temperature thermal model

12. Moscow (20/12 - 24/12, 2004) 12 Cosmology and High Energy Astrophysics (Zeldovich 90) T spec Fitting two-temperature thermal spectra with single-temperature models: Z=1 T=10 keV T=1 keV T=2.5 keV T=5 keV T spec

13. Moscow (20/12 - 24/12, 2004) 13 Cosmology and High Energy Astrophysics (Zeldovich 90) Tew v.s. Tspec: Z=1 T ew Overpredicts T spec Discrepancies as large as 60% Because of line emission, the two temperature source spectra can be fitted by a single temperature thermal model If T 1 >3 keV

14. Moscow (20/12 - 24/12, 2004) 14 Cosmology and High Energy Astrophysics (Zeldovich 90) A new projected temperature: spectroscopic-like temperature We want: We expand in Taylor series We find The extension of to a continuum distribution of plasma in is:

15. Moscow (20/12 - 24/12, 2004) 15 Cosmology and High Energy Astrophysics (Zeldovich 90) A new projected temperature: spectroscopic-like temperature The unknown function depends mainly on the temperature and can be approximated by: It needs to be calibrated on the instrument used and the observation “conditions”. This is done by minimizing the discrepancy with T spec Value of  that minimize  Error bars: range in  for which  <4% We can find a “universal” value:  = 0.75

16. Moscow (20/12 - 24/12, 2004) 16 Cosmology and High Energy Astrophysics (Zeldovich 90) A new projected temperature: spectroscopic-like temperature There is a temperature bias toward the low temperature dominant components Mazzotta, P., Rasia, E., Moscardini, L., & Tormen, G. 2004, MNRAS, 354, 10

17. Moscow (20/12 - 24/12, 2004) 17 Cosmology and High Energy Astrophysics (Zeldovich 90) T sl v.s. T spec Z=0 Z= 1

18. Moscow (20/12 - 24/12, 2004) 18 Cosmology and High Energy Astrophysics (Zeldovich 90) Now What? Lets see some Consequences

19. Moscow (20/12 - 24/12, 2004) 19 Cosmology and High Energy Astrophysics (Zeldovich 90) Astrophysical Implications Mazzotta, P., Rasia, E., Moscardini, L., & Tormen, G. 2004, MNRAS, 354, 10

20. Moscow (20/12 - 24/12, 2004) 20 Cosmology and High Energy Astrophysics (Zeldovich 90) N-body Temperature Maps Emission-Weighted Spectroscopic-Like Shock fronts No Shock fronts

21. Moscow (20/12 - 24/12, 2004) 21 Cosmology and High Energy Astrophysics (Zeldovich 90) Temperature Map of the “observed” N-body cluster We We built a simulator of Chandra observations: X-MAS (X-ray map simulator) Gardini et al. 2003 astro ph/0310844 X-MAS X-MAS uses ad input N-body simulations and give in output photon event files similar to real observations Output Output of X-MAS can be treated as a real observations: it can be analyzed using the same tools and techniques We We generated a 300 ks Chandra “observation” of the N-body cluster

22. Moscow (20/12 - 24/12, 2004) 22 Cosmology and High Energy Astrophysics (Zeldovich 90) Comparison between T spec,T ew,T sl T ew T sl

23. Moscow (20/12 - 24/12, 2004) 23 Cosmology and High Energy Astrophysics (Zeldovich 90) Temperature Profile of N-body simulation Data analysis of the Chandra “observation” of the simulated cluster obtained with X-MAS T ew T spec

24. Moscow (20/12 - 24/12, 2004) 24 Cosmology and High Energy Astrophysics (Zeldovich 90) Temperature Profile of a real Cluster (2A 0335) T ew T sl Mazzotta., Edge, Markevitch 2003, ApJ, 596, 190

25. Moscow (20/12 - 24/12, 2004) 25 Cosmology and High Energy Astrophysics (Zeldovich 90) Cosmological Implications E. RasiaE. Rasia, P. Mazzotta, S. Borgani, L. Moscardini, K. Dolag, G. Tormen, A. Diaferio, G. Murante, 2005 ApJL, 618, L1P. MazzottaS. BorganiL. MoscardiniK. DolagG. TormenA. DiaferioG. Murante

26. Moscow (20/12 - 24/12, 2004) 26 Cosmology and High Energy Astrophysics (Zeldovich 90) Cosmological Implications T x T x Depends on the thermal complexity of the cluster: merging history As As T x <T ew, T x <T ew, it it may substantially influence the M-T relation The The observed N(T) function may thus be lower than what predicted by N-body simulations This This may result in underestimate of 8888 We We used the key-project simulation ( Borgani ( Borgani et al. 2004, MNRAS, 348, 1078 ): 1078 ): high resolution CDM+L hydro-SPH with cooling and feedback

27. Moscow (20/12 - 24/12, 2004) 27 Cosmology and High Energy Astrophysics (Zeldovich 90) Results on the M-T relation E. Rasia, et al. 2005 ApJL, 618, L1 We used the key-project simulation: high resolution CDM+L hydro-SPH with cooling and feedback  8 This tells that the value of  8 estimated from the N(T) relation represents un underestimate of the true value

28. Moscow (20/12 - 24/12, 2004) 28 Cosmology and High Energy Astrophysics (Zeldovich 90) The Temperature Function Concordance model With  8 =0.8 and T ew Same model but using T sl In our case 88 should increase from 0.8 => 0.9

29. Moscow (20/12 - 24/12, 2004) 29 Cosmology and High Energy Astrophysics (Zeldovich 90)Conclusions Projected Projected spectroscopic temperature T spec T spec of thermally complex clusters obtained from X-ray observations is always lower than the emission-weighed temperature T ew. This This temperature bias is mainly related to the fact that the emission-weighted temperature does not reflect the actual spectral properties of the observed source. Aproper comparison between simulations and observations needs the actual simulations of spectral properties of the simulated clusters. Nevertheless, if the cluster temperatures is >3 keV it is possible to define a temperature function, that we call spectroscopic-like temperature T sl, T sl, which approximate T spec T spec to better than few per cent. Using Using hydrodynamical simulations of galaxy clusters, we find that T sl T sl is lower than T ew by 20-30%. As As previous study made using T ew T ew shows that the discrepancy in the M-T relation between simulations and observations is about 20 per cent, it is clear that the use of T sl increases this discrepancy to 50%. Nevertheless, Nevertheless, if we assume hydrostatic equilibrium for the gas density distribution described by a  -model  -model with a polytropic equation of state, we know that masses are underestimated on average by 40%. Although Although this goes in the direction of substantially reducing the discrepancy with observational data this is not sufficient to cancel it. The The bias in the M-T relation propagates into a bias in  8,  8, from the XTF. If such a bias is as large as that found in our simulations, the values of 8 8 8 8 obtained by combining the local XTF and the observed M-T relation are underestimated by about 15 per cent. The The XTF from the simulation is significantly lower when using T sl T sl instead of Tew. A comparison with the observed XTF indicates that for the ``concordance'' CDM model needs to be increased from 0.8 to 0.9. To To conclude, the results of this study go in the direction of alleviating a possible tension between the power-spectrum normalization obtained from the number density of galaxy clusters and that arising from the first-year WMAP CMB anisotropies.

30. Moscow (20/12 - 24/12, 2004) 30 Cosmology and High Energy Astrophysics (Zeldovich 90) Comparison of Mass estimation techniques through X-ray mass measurements of “observations” of Hydro simulations Warning: Very preliminary results!!!!!!!

31. Moscow (20/12 - 24/12, 2004) 31 Cosmology and High Energy Astrophysics (Zeldovich 90) THE END

32. Moscow (20/12 - 24/12, 2004) 32 Cosmology and High Energy Astrophysics (Zeldovich 90) Conclusions 1/2 the the projected spectroscopic temperature is not a well defined quantity In In principle a proper comparison between observations and simulations requires also the simulation of the “observation” of the latter For For this reason we developed X-MAS: a simulator of X-ray observations to be applied at the output of the N-body cluster simulation. Its main characteristics is that it produces an event file which is equivalent to a real observation. observation. We plan to make this simulator public available in one year time. In the meanwhile (and in case you do not like to do data analysis of simulated cluster) there are three news: a good one a two bad ones

33. Moscow (20/12 - 24/12, 2004) 33 Cosmology and High Energy Astrophysics (Zeldovich 90) Conclusions 2/2 Good Good news: If If T>3keV, for Chandra and XMM T spec T spec is defined. Bad Bad News: 1) 1) T ew T ew gives a misleading idea of what an observer can and will measure 2) 2) If T>3keV, for Chandra and XMM T spec T spec is defined. Thus, Thus, continue to use T mw T mw (at least it has a physical meaning) but please do not use T ew T ew to describe the projected temperature of your simulations. Observed Observed X-ray temperatures are biased toward the lower temperature thermal components of the source spectrum: shock fronts may easily be hidden by this bias The value of 88 88 estimated from the N(T) relation represents un underestimate of the true value