p. mazzotta university of roma “tor vergata” and harvard-smithsonian center for astrophysics

Moscow(20/12 - 24/12, 2004) 1

Cosmology and High Energy Astrophysics (Zeldovich 90)

Comparing the Comparing the temperatures of Galaxy temperatures of Galaxy

Clusters from hydro-N-body Clusters from hydro-N-body simulations to simulations to ChandraChandra and and

XMM observationsXMM 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

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Common misconceptions about temperatures

Outline of the talkOutline of the talk

I will introduce a new temperature estimator that better approximate the projected X-ray temperature

Common misconceptions: projected X-ray temperature = Tew

Discuss some (cosmological) implications for the determination of 8 via the XTF

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Projected Gas Projected Gas TemperatureTemperature

Gas temperature distribution

One (or more)Observer(s)

Projected gas temperature

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Temperature maps of Temperature maps of simulated Clusterssimulated Clusters

Nagai & Kravtsov, 2002, ApJL

T

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Temperature maps of Temperature maps of Clusters Observed with Clusters Observed with

ChandraChandraMKW 3S A3667 2A 0335

Mazzotta et al. 2002, ApJL, 567, 37 Mazzotta et al. 2002, ApJL, 269, 31 Mazzotta et al. 2003, ApJ, 596, 190

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How do we compare How do we compare temperature maps temperature maps

obtained from Hydro+N-obtained from Hydro+N-body simulationbody simulation

with the ones obtained with the ones obtained from the data analysis of from the data analysis of

X-ray observations?X-ray observations?

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Temperature from hydro-N-body Temperature from hydro-N-body simulations: simulations:

mass and emission-weighted mass and emission-weighted

temperaturetemperature 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

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Spectroscopic projected Spectroscopic projected temperature temperature

From an X-ray observation point of view From an X-ray observation point of view the cluster gas temperature is derived the cluster gas temperature is derived through the fit of a thermal model to the through the fit of a thermal model to the observed spectrum. observed spectrum.

Measuring a projected temperature is thus Measuring a projected temperature is thus equivalent to find a thermal model with a equivalent to find a thermal model with a temperature Ttemperature Tspecspec whose spectral whose spectral properties are as close as possible to the properties are as close as possible to the properties of the projected spectra. properties of the projected spectra.

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Spectroscopic projected Spectroscopic projected temperaturetemperature

The emission spectrum can be written as:

The combination of two thermal bremsstrahlung is not a thermal bremsstrahlung

Tspec 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

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TspecTspec

Fitting two-temperature thermal Fitting two-temperature thermal spectra with single-temperature spectra with single-temperature

models: Z=0models: Z=0 T=10 keV T=10 keVT=10 keV

T=1 keV T=2.5 keV T=5 keV

Tspec

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TTewew v.s. T v.s. Tspecspec: Z=0: Z=0

Tew Overpredicts Tspec

Discrepancies as large as 60%

If T1>2 keV the two temperature source spectra can be fitted by a single temperature thermal model

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TspecTspec

Fitting two-temperature thermal Fitting two-temperature thermal spectra with single-temperature spectra with single-temperature

models: Z=1models: Z=1 T=10 keV T=10 keV

T=10 keV

T=1 keV T=2.5 keV T=5 keV

Tspec

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Tew v.s. Tspec: Z=1Tew v.s. Tspec: Z=1

Tew Overpredicts Tspec Discrepancies as large as 60%

Because of line emission, the two temperature source spectra can be fitted by a single temperature thermal model If T1>3 keV

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A new projected A new projected temperature:temperature:

spectroscopic-like spectroscopic-like temperature temperature We want:

We expand in Taylor series

We findThe extension of to a continuum distribution of plasma in is:

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spectroscopic-like spectroscopic-like temperature temperature

TTZ ),(

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 Tspec

Value of that minimize

Error bars: range in for which <4%

We can find a “universal” value: = 0.75

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spectroscopic-like spectroscopic-like temperaturetemperature

2

4/3T

nw

wdV

wTdVTsl

2/12Tnw

wdV

wTdVTew

There is a temperature bias toward the low temperature dominant components

Mazzotta, P., Rasia, E., Moscardini, L., & Tormen, G. 2004, MNRAS,

354, 10

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TTslsl v.s. T v.s. Tspecspec

Z=0Z=0 Z=Z=11

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Now What?Now What?

Lets see someLets see someConsequencesConsequences

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AstrophysicAstrophysical al

ImplicationsImplications Mazzotta, P., Rasia, E., Moscardini, L., & Tormen, G. 2004, MNRAS,

354, 10

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N-body Temperature N-body Temperature MapsMaps

Emission-Weighted Spectroscopic-Like

Shock fronts No Shock fronts

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Temperature Map of the Temperature Map of the “observed” N-body cluster“observed” N-body cluster

We built a simulator of Chandra We built a simulator of Chandra observations: X-MAS (X-ray map observations: X-MAS (X-ray map

simulator) simulator) Gardini et al. 2003 astro ph/0310844Gardini et al. 2003 astro ph/0310844

X-MAS uses ad input N-body X-MAS uses ad input N-body simulations and give in output simulations and give in output photon event files similar to real photon event files similar to real observations observations

Output of X-MAS can be treated as Output of X-MAS can be treated as a real observations: it can be a real observations: it can be analyzed using the same tools and analyzed using the same tools and techniquestechniques

We generated a 300 ks Chandra We generated a 300 ks Chandra “observation” of the N-body “observation” of the N-body clustercluster

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Comparison between Comparison between TTspecspec,T,Tewew,T,Tsl sl

TTewew

TTslsl

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Temperature Profile of N-Temperature Profile of N-body simulationbody simulation

Data analysis of the Chandra “observation” of the simulated cluster obtained with X-MAS

Tew

Tspec

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Temperature Profile of a Temperature Profile of a real Cluster (2A 0335)real Cluster (2A 0335)

TewTsl

Mazzotta., Edge, Markevitch 2003, ApJ, 596, 190

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CosmologiCosmological cal

ImplicationImplicationss

E. Rasia, P. Mazzotta, S. Borgani, L. Moscardini, K. Dolag, G. Tormen, A. Diaferio, G. Murante, 2005 ApJL, 618, L1

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Cosmological Cosmological ImplicationsImplications

TTxx Depends on the thermal complexity of the Depends on the thermal complexity of the cluster: merging historycluster: merging history

As TAs Txx<T<Tewew, it, it may substantially influence the M-T may substantially influence the M-T relationrelation

The observed N(T) function may thus be lower The observed N(T) function may thus be lower than what predicted by N-body simulationsthan what predicted by N-body simulations

This may result in underestimate of This may result in underestimate of 88

We used the key-project simulation (We used the key-project simulation (Borgani et al. Borgani et al. 2004, MNRAS, 348, 10782004, MNRAS, 348, 1078): high resolution CDM+L ): high resolution CDM+L hydro-SPH with cooling and feedbackhydro-SPH with cooling and feedback

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Results on the M-T relationResults on the M-T relation

E. Rasia, et al. 2005 ApJL, 618, L1 We used the key-project We used the key-project

simulation: high simulation: high

resolution CDM+L hydro-resolution CDM+L hydro-

SPH with cooling and SPH with cooling and

feedbackfeedback

This tells that the value of 88 estimated from the N(T) relation

represents un underestimate of the true value

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The Temperature The Temperature FunctionFunction

Concordance model

With 8=0.8 and Tew

Same model but

using Tsl

In our case 8 should increasefrom 0.8 => 0.9

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ConclusionsConclusions Projected spectroscopic temperature TProjected spectroscopic temperature Tspecspec of thermally complex clusters obtained of thermally complex clusters obtained

from X-ray observations is always lower than the emission-weighed temperature Tfrom X-ray observations is always lower than the emission-weighed temperature T ewew. . This temperature bias is mainly related to the fact that the emission-weighted 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. temperature does not reflect the actual spectral properties of the observed source. A proper comparison between simulations and observations needs the actual A proper comparison between simulations and observations needs the actual

simulations of spectral properties of the simulated clusters. Nevertheless, if the 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 cluster temperatures is >3 keV it is possible to define a temperature function, that we call spectroscopic-like temperature Twe call spectroscopic-like temperature Tslsl, which approximate T, which approximate Tspecspec to better than to better than few per cent. few per cent.

Using hydrodynamical simulations of galaxy clusters, we find that TUsing hydrodynamical simulations of galaxy clusters, we find that T slsl is lower than is lower than TTewew by 20-30%. by 20-30%.

As previous study made using TAs previous study made using Tewew shows that the discrepancy in the M-T relation 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 between simulations and observations is about 20 per cent, it is clear that the use of TTslsl increases this discrepancy to 50%. increases this discrepancy to 50%.

Nevertheless, if we assume hydrostatic equilibrium for the gas density distribution Nevertheless, if we assume hydrostatic equilibrium for the gas density distribution described by a described by a -model with a polytropic equation of state, we know that masses are -model with a polytropic equation of state, we know that masses are underestimated on average by 40%. underestimated on average by 40%.

Although this goes in the direction of substantially reducing the discrepancy with Although this goes in the direction of substantially reducing the discrepancy with observational data this is not sufficient to cancel it. observational data this is not sufficient to cancel it.

The bias in the M-T relation propagates into a bias in The bias in the M-T relation propagates into a bias in 88, from the XTF. If such a bias , from the XTF. If such a bias is as large as that found in our simulations, the values of is as large as that found in our simulations, the values of 88 obtained by combining obtained by combining the local XTF and the observed M-T relation are underestimated by about 15 per the local XTF and the observed M-T relation are underestimated by about 15 per cent. cent.

The XTF from the simulation is significantly lower when using TThe XTF from the simulation is significantly lower when using T slsl instead of Tew . A instead of Tew . A comparison with the observed XTF indicates that for the ``concordance'' CDM model comparison with the observed XTF indicates that for the ``concordance'' CDM model needs to be increased from 0.8 to 0.9. needs to be increased from 0.8 to 0.9.

To conclude, the results of this study go in the direction of alleviating a possible 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 tension between the power-spectrum normalization obtained from the number density of galaxy clusters and that arising from the first-year WMAP CMB anisotropies.density of galaxy clusters and that arising from the first-year WMAP CMB anisotropies.

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Comparison of Mass Comparison of Mass estimation techniques through estimation techniques through X-ray mass measurements of X-ray mass measurements of

“observations” of Hydro “observations” of Hydro simulationssimulations

Warning: Very preliminary results!!!!!!!

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THE ENDTHE END

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Conclusions 1/2Conclusions 1/2

the projected spectroscopic temperature is not a the projected spectroscopic temperature is not a well defined quantity well defined quantity

In principle a proper comparison between In principle a proper comparison between observations and simulations requires also the observations and simulations requires also the simulation of the “observation” of the lattersimulation of the “observation” of the latter

For this reason we developed X-MAS: a simulator For this reason we developed X-MAS: a simulator of X-ray observations to be applied at the output of X-ray observations to be applied at the output of the N-body cluster simulation. Its main of the N-body cluster simulation. Its main characteristics is that it produces an characteristics is that it produces an event file event file which is equivalent to a real observation.which is equivalent to a real observation. We plan We plan to make this simulator public available in one to make this simulator public available in one year time.year time.

In the meanwhile (and in case you do not like to In the meanwhile (and in case you do not like to do data analysis of simulated cluster) there are do data analysis of simulated cluster) there are three news: a good one a two bad onesthree news: a good one a two bad ones

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Conclusions 2/2Conclusions 2/2

Good news:Good news: If T>3keV, for Chandra and XMM TIf T>3keV, for Chandra and XMM Tspec spec is defined.is defined. Bad News:Bad News: 1) T1) Tew ew gives a misleading idea of what an observer can and gives a misleading idea of what an observer can and

will measurewill measure 2) If T>3keV, for Chandra and XMM T2) If T>3keV, for Chandra and XMM Tspec spec is defined.is defined. Thus, continue to use TThus, continue to use Tmwmw (at least it has a physical (at least it has a physical

meaning) but please do not use Tmeaning) but please do not use Tewew to describe the to describe the projected temperature of your simulations.projected temperature of your simulations.

Observed X-ray temperatures are biased toward the lower Observed X-ray temperatures are biased toward the lower temperature thermal components of the source spectrum: temperature thermal components of the source spectrum: shock fronts may easily be hidden by this biasshock fronts may easily be hidden by this bias

The value of 88 estimated from the N(T) relation represents un underestimate of the true value

p. mazzotta university of roma “tor vergata” and harvard-smithsonian center for astrophysics

Documents

temperature tspec

temperature thermal

new projected temperature

temperature source spectra

cluster gas temperature

singletemperature models

new temperature estimator

observed temperature